Mastering Physics Solutions Chapter 31 Atomic Physics

Mastering Physics Solutions Chapter 31 Atomic Physics

Mastering Physics Solutions

Chapter 31 Atomic Physics Q.1CQ
Give areason why the Thomson plum-pudding model does not agree with experimental observations.
Solution:
Experimental observations that Thomson plum – pudding model does not agree.
1) Thomson observed only one spectral line by his assumption while experimental observation reveals that hydrogen spectrum consists of five different series with several lines in each series.
2) This model could not provide any satisfactory mechanism for explaining the large deflection suffered by – particles in Rather-ford’s experiment.

Chapter 31 Atomic Physics Q.1P
The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10−11 m from the nucleus, which has a diameter of about 1.0 × 10−15 m. If you. assume the hydrogenatom to be a sphere of radius 5.3 × 10−11 m, what fraction of its volume is occupied by the nucleus?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics1ps

Chapter 31 Atomic Physics Q.2CQ
Give a reason why the Rutherford solar-system model does not agree with experimental observations.
Solution:
According to Rutherford atomic model, electrons revolve round the nucleus in circular orbits. Such a revolving electron will lose its energy continuously and it falls into the nucleus after a certain instant of time. Therefore, the atom gets collapsed. This is in contradiction with the practical observations which shows atoms are stable. Due to this reason Rutherford solar system model does not agree with experimental observation.

Chapter 31 Atomic Physics Q.2P
Referring to Problem 1, suppose the nucleus of the hydrogen atom were enlarged to the size of a baseball (diameter = 7.3 cm). At what typical distance from the center of the baseball would you expect to find the electron?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics2ps
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Chapter 31 Atomic Physics Q.3CQ
Cite one example of how the Bohr model disagrees with the quantum mechanical model of the hydrogen atom.
Solution:
According to Bohr’s theory we have only energy level for an electron. When there are some electrons in a state ‘n’ then all these electrons are equidistant from the centre of the atom.
But in quantum theory, we have sub levels and sub – sub levels of an electron. So the electrons need not to be equidistant from the centre of the atom even though they are in the same state ‘n’. This is one example out of several that Bohr model disagrees with the quantum mechanical model of hydrogen atoms.

Chapter 31 Atomic Physics Q.3P
Copper atoms have 29 protons in their nuclei. If the coppernucleus is a sphere with a diameter of 4.8 × 10−15 m, find the work required to bring an alpha particle (charge = +2e) from rest at infinity to the “surface” of the nucleus.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics3ps
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Chapter 31 Atomic Physics Q.4CQ
What observation led Rutherford to propose that atoms have a small nucleus containing most of the atom’s mass?
Solution:
When conducting the experiment of α-particle scattering, surprisingly he observed few particles turned back towards source itself. This result led to the idea that there must be a great concentration of positive charge and mass within an atom.

Chapter 31 Atomic Physics Q.4P
In Rutherford’s scattering experiments, alpha particles (charge = +2e) were fired at a gold foil. Consider an alpha particle with an initial kinetic energy K heading directly for the nucleus of a gold atom (charge = +79e). The alpha particle will come to rest when all its initialkinetic energy has been converted to electrical potential energy. Find the distance of closest approachbetween the alpha particle and the gold nucleus for the case K = 3.0 MeV.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics4ps
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Chapter 31 Atomic Physics Q.5CQ
Do yon expect the light given off by (a) a neon sign or (b) an Incandescent lightbulb to be continuous in distribution, or in the form of a line spectrum? Explain.
Solution:
a) A neon sign is obtained when neon gas under a low pressure is applied with high voltage. As the glass tube of a neon sign contains a low – pressure gas we expect that the light from the sign to be in the form of a line spectrum.
b) But in incandescent bulb the light is emitted by the burning of the filament. Therefore the radiation is the black body radiation from a hot object. Therefore, its radiation is distributed as a continuous distribution.

Chapter 31 Atomic Physics Q.5P
Find the wavelength of the Balmer series spectra! line corresponding to n = 15.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics5ps

Chapter 31 Atomic Physics Q.6CQ
In principle, how many spectral lines are there inany given series of hydrogen? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics6cqs

Chapter 31 Atomic Physics Q.6P
What is the smallest value of n for which the wavelength of a Balmer scries line is less than 400 mm?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics6ps
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Chapter 31 Atomic Physics Q.7CQ
Is there an upper limit to the radius of an allowed Bohr orbit? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics7cqs

Chapter 31 Atomic Physics Q.7P
Find the wavelength of the three longest-wavelength lines of the Lyman series.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics7ps
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Chapter 31 Atomic Physics Q.8CQ
(a) Is there an upper limit to the wavelength of lines in. the spectrum of hydrogen? Explain. (b) Is there a lower limit? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics8cqs

Chapter 31 Atomic Physics Q.8P
Find the wavelength of the three longest-wavelength lines of the Paschen series.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics8ps
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Chapter 31 Atomic Physics Q.9CQ
The principal quantum number, n, can increase without limit in the hydrogen atom. Does this mean that the energy of the hydrogen atom also can increase without limit? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics9cqs

Chapter 31 Atomic Physics Q.9P
Find (a) the longest wavelength in the Lyman series and (b) the shortest wavelength in the Paschen series.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics9ps
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Chapter 31 Atomic Physics Q.10CQ
For each of the following configurations of outermost electrons, state whether the configuration is allowed by the rules of quantum mechanics. If the configuration is not allowed, give the rule or rules that are violated, (a) 2d1, (b) 1p7,(c) 3p5, (d) 4g6
Solution:
mastering-physics-solutions-chapter-31-atomic-physics10cqs

Chapter 31 Atomic Physics Q.10P
In Table 31-1 we see that the Paschen series corresponds to n’ = 3 in Equation 31-2, and that the Brackett series corresponds to n’ = 4. (a) Showthat the ranges of wavelengths of these two series overlap, (b) Is there a similaroverlap between the Balmer series and the Paschen series? Verify your answer.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics10ps
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Chapter 31 Atomic Physics Q.11CQ
(a) In the quantummechanical model of the hydrogen atom, there is one value of n for which the angular momentum of the electron must be zero. What is this value of n?(b) Can the angular momentum of the electron be zero in states with other values of it? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics11cqs

Chapter 31 Atomic Physics Q.11P
CE Predict/Explain (a) If the mass of the electron were magically doubled, would the ionization energy of hydrogenincrease, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The ionization energy would increase because the increased mass would mean the electron would orbit closer to the nucleus and would require more energy to move to infinity.
II. The ionization energy would decrease because a more massive electron is harder to hold in orbit, and therefore it is easier to remove the electron and leave the hydrogen ionized.
III. The ionizarioii energy would be unchanged because, just like in gravitational orbits, the orbit of the electron is independent of its mass. As a result, there is no change in the energy required to move it to infinity.
Solution:
(a) If the mass of the electron were magically doubled, than ionization energy of hydrogen would have increase.
(b) The ionization energy would increase because the increased mass would mean the electron would orbit closer to the nucleus and require more energy to move to infinity.
Therefore option I is the best explanation

Chapter 31 Atomic Physics Q.12CQ
Would you expect characteristic X-rays to be emitted, by (a) helium atoms or (b) lithium atoms in their ground state? Explain.
Solution:
Characteristic X ray spectrum of a particular element is observed when an electron in the inner shell is removed from the atom, and an electron from the outer shell occupies the vacant place in the inner shell. Therefore, atoms in the ground state cannot emit characteristic X ray spectrum. Even though if an electron from excited state reaches the ground state does not result an X ray spectrum because the binding energy of He and Li atoms is very much less than the energy of the characteristic X ray spectrum.
Therefore, characteristic X ray spectrum cannot be expected from He and Li atoms that are in ground state.

Chapter 31 Atomic Physics Q.12P
CE Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 2; (B) singly ionized helium in the state n = 1; (C) doubly ionized lithium in the state n = 3. Rank these three atoms in order of increasing Bohr radius. Indicate ties where appropriate.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics12ps

Chapter 31 Atomic Physics Q.13CQ
The elements fluorine, chlorine, and bromine are found to exhibit similar chemical properties. Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics13cqs

Chapter 31 Atomic Physics Q.13P
CE Consider the Bohr model as applied to the following three atoms: (A) neutral hydrogen in the state n = 3; (B) singly ionized helium in the state n = 2; (C) doubly ionized lithium in the state n = 1. Rank these tliree atoms in order of increasing energy. Indicate ties where appropriate.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics13ps

Chapter 31 Atomic Physics Q.14P
An electron in the n = 1 Bohr orbit has the kinetic energy K1. In terms of K1, what is the kinetic energy of an electron in the n = 2 Bohr orbit?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics14ps

Chapter 31 Atomic Physics Q.15P
Find the ratio v/c for an electron in the first excited state(n = 2) of hydrogen.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics15ps

Chapter 31 Atomic Physics Q.16P
Find the magnitude of the force exerted on an electron in the ground-state orbit of the Bohr model.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics16ps

Chapter 31 Atomic Physics Q.17P
How much energy is required to ionize hydrogen when it is in the n = 4 state?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics17ps

Chapter 31 Atomic Physics Q.18P
Find the energy of the photon required to excite a hydrogen atom from the n = 2 state to the n = 5 state.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics18ps

Chapter 31 Atomic Physics Q.19P
In the Bohr model, the potential energy of a hydrogen atom in the nth orbit has a value we will call Un. What is the potential energy of a hydrogen atom when the electron is in the (n + 1)th Bohr orbit? Give your answer in terms of Un and n.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics19ps

Chapter 31 Atomic Physics Q.20P
A hydrogen atom is in its second excited state, n = 3. Using the Bohr model of hydrogen, find (a) the linear momentum and (b) the angular momentum of the electron in this atom.
Solution:
Given the hydrogen atom is in the n = 3 state
mastering-physics-solutions-chapter-31-atomic-physics20ps

Chapter 31 Atomic Physics Q.21P
Referring to Problem 20, find (a) the kinetic energy of the electron, (b) the potential energy of the atom, and (c) the total energy of the atom. Give your resul ts in eV.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics21ps
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Chapter 31 Atomic Physics Q.22P
Initially, an electron is in the n = 3 state of hydrogen. If this electron acquires an additional 1.23 eV ofenergy, what is the value of n in the final state of the electron?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics22ps

Chapter 31 Atomic Physics Q.23P
Identify the initiai and final states if an electron in hydrogen emits a photon with a wavelength of 656 mm.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics23ps
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Chapter 31 Atomic Physics Q.24P
IP An electron in hydrogen absorbs a photon and jump to a higherorbit, (a) Find the energy the photon must have in the initial state is n = 3 and the final state is n = 5. (b) If the initial state was n = 5and the final state n = 7, would the energy of the photon be greater than, less than, or the same as that found in part (a)? Explain, (c) Calculate the photon energy for part (b).
Solution:
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Chapter 31 Atomic Physics Q.25P
IP Consider the following four transitions in a hydrogen atom:
(i) ni = 2, nf = 6
(ii) ni = 2, nf = 8
(iii) ni = 7, nf = 8
(iv) ni = 6, nf = 2
Solution:
mastering-physics-solutions-chapter-31-atomic-physics25ps
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mastering-physics-solutions-chapter-31-atomic-physics25ps2
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Chapter 31 Atomic Physics Q.26P
IP Muonitun Muonium is a hydrogen-like atom inwhich the electronis replaced with a muon, a fundamentalparticle with a charge of — e and a mass equal to 207me. (The muon is sometimes referred to loosely as a “heavy electron.”) (a) What is the Bohr radius of muonium? (b) Will the wavelengths in the Balmer series of muonium be greater than, less than, or the same as the wavelengths in the Baimer series of hydrogen? Explain, (c) Calculate the longest wavelength of the Balmer series in muonium.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics26ps
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Chapter 31 Atomic Physics Q.27P
IP (a) Find the radius of the n = 4 Bohr orbit of a doubly ionized lithium atom (Li2+, Z = 3). (b) Is the energy required to raise an electron from the n =4 state to the n = 5 state in Li2+ greatest than, less than, or equal to the energy requiredto raise an electron in hydrogen from the n = 4 state to the n = 5 state? Explain, (c) Verify your answer to part(b) by calculating the relevan t energies.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics27ps
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Chapter 31 Atomic Physics Q.28P
Applying the Bohr model to a triply ionized beryllium atom (Be3+, Z = 4), find (a) the shortest wavelength of the Lyman scries for Be3+ and (b) the ionization energy required to remove the final electron in Be3+.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics28ps
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Chapter 31 Atomic Physics Q.29P
(a) Calculate the time required for an electron in the n = 2 state of hydrogen to complete one orbit about the nucleus, (b) The typical “lifetime” of an electron in the n = 2 state is roughly 10−8 s—after this time the electron is likely to have dropped back to the n = 1 stale. Estimate the number of orbits an election completes in the n = 2 state before dropping to the groundstate.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics29ps
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Chapter 31 Atomic Physics Q.30P
IP The kinetic energy of an electron in a particular Bohr orbit of hydrogen is l.35 × 10−19 J. (a) Which Bohr orbit does the electron occupy? (b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the kinetic energy of the electron increase, decrease, or stay the same? Explain. (c) Calculate the kinetic energy of the electron in the orbit referred to in part (b).
Solution:
mastering-physics-solutions-chapter-31-atomic-physics30ps
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Chapter 31 Atomic Physics Q.31P
IP The potential energy of a hydrogen atom in a particular Bohr orbit is − 1.20 × 10−9 J. (a) Which Bohr orbit does the electron occupy in this atom? (b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the potential energy of the atom increase, decrease, or stay the same? Explain. (c) Calculate the potential energy of the atom for the orbit referred to in part (b).
Solution:
mastering-physics-solutions-chapter-31-atomic-physics31ps
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Chapter 31 Atomic Physics Q.32P
Consider a head-on collision between two hydrogen atoms, both initially in their ground state and moving with the same speed. Find the minimum speed necessary to leave both atoms in their n = 2state after the collision.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics32ps
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Chapter 31 Atomic Physics Q.33P
Ahydrogen atom is in the initial state n1 = n, where n > 1. (a) Find the frequency of the photon that is emitted when the electron jumps to state nf − n − 1. (b) Find the frequency of the electron’s orbital motion in the state n. (c) Compare your results for parts (a) and (b) in the limit of large n.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics33ps
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Chapter 31 Atomic Physics Q.34P
CE Predict/Explain (a) Is the de Broglie wavelength of an electron in the n = 2 Bohr orbit of hydrogen greater than, less than, or equal to the de Broglie wavelength in the n = 1 Bohr orbit? (b) Choose the best explanation from among the following:
I. The de Broglie wavelength in the nth state is 2πr/n,where r is proportional to n2. Therefore, the wavelength increases with increasing n, and is greater for n = 2 than for n = 1.
II. The de Broglie wavelength of an electron in the n thstate is such that n wavelengths fit around the circumference of the orbit. Therefore, λ = 2πr/n and the wavelength for n = 2 is less than for n = 1.
III. The de Broglie wavelength depends on the mass of the electron, and that is the same regardless of which state of the hydrogen atom the election occupies.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics34ps

Chapter 31 Atomic Physics Q.35P
Find the de Broglie wavelength of an electron in the ground state of the hydrogen atom.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics35ps
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Chapter 31 Atomic Physics Q.36P
Find an expression for the de Broglie wavelength of an electron in the nth state of the hydrogen atom.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics36ps
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Chapter 31 Atomic Physics Q.37P
What is the radius of the hydrogen-atom Bohr orbit shown in Figure?
mastering-physics-solutions-chapter-31-atomic-physics37p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics37ps
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Chapter 31 Atomic Physics Q.38P
(a) Find the kinetic energy (in eV) of an electron whose de Broglie wavelength is equal to 0.5 Å, a typical atomic size, (b) Repeat part (a) for an electron with a wavelength equal to 10−15 m, a typical nuclear size.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics38ps
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Chapter 31 Atomic Physics Q.39P
What are the allowed values of ℓ when the principal quantum number is n = 5?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics39ps

Chapter 31 Atomic Physics Q.40P
How many different values of mℓ are possible when the principal quantum number is n = 4?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics40ps

Chapter 31 Atomic Physics Q.41P
mastering-physics-solutions-chapter-31-atomic-physics41pSolution:
mastering-physics-solutions-chapter-31-atomic-physics41ps
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Chapter 31 Atomic Physics Q.42P
IP Hydrogen atom number 1is known to be in the 4/state.
(a) What is the energy of this atom? (b) What is the magnitude of this atom’s orbital angular momentum? (c) Hydrogen atom number 2 is in the 5d state. Ts this atom’s energy greater than, less than, or the same as that of atom 1? Explain. (d) Is the magnitude of the orbital angular momentum of atom 1 greater than, less than, or the same as that of atom 2? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics42ps
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Chapter 31 Atomic Physics Q.43P
mastering-physics-solutions-chapter-31-atomic-physics43p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics43ps
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Chapter 31 Atomic Physics Q.44P
IP The electron in a hydrogen atom with an energy of —0.544 eV is in a subshell with 18 states. (a) What is the principal quantum number, n, for this atom? (b) What is the maximum possible orbital angular momentum this atom can have? (c) Is the number of states in the subshell with the next lowest value of t equal to 16, 14, or 12? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics44ps
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Chapter 31 Atomic Physics Q.45P
IP Consider two different states of a hydrogen atom. In state I the maximum value of the magnetic quantum number is nij = 3; in state II the corresponding maximum value is tttf = 2. Let Lj and L^ represent the magnitudes of the orbital angular momentum of an electron in states T and II, respec-. tively. (a) Is Lj greater than, less than, or equal to Ljf? Explain.
(b) Calculate the ratio Lj/Ln.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics45ps
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Chapter 31 Atomic Physics Q.46P
CE How many eiectrons can occupy (a) the 2p subshell and (b) the 3p subshell?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics46ps

Chapter 31 Atomic Physics Q.47P
CE (a) How many eiectrons can occupy the 3d subshell? (b) How many electrons can occupy the n = 2shell?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics47ps

Chapter 31 Atomic Physics Q.48P
mastering-physics-solutions-chapter-31-atomic-physics48p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics48ps

Chapter 31 Atomic Physics Q.49P
Give the electronic configuration for the ground state of carbon.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics49ps

Chapter 31 Atomic Physics Q.50P
List the values of the four quantum numbers (n, ℓ, mℓ, ms)for each of the electrons in the ground state of neon.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics50ps
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Chapter 31 Atomic Physics Q.51P
Give the electronic configuration for the ground state of nitrogen.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics51ps

Chapter 31 Atomic Physics Q.52P
Give a list of all possible sets of the four quantum numbers (n, ℓ, mℓ, ms) for electrons in the 3s subshell.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics52ps

Chapter 31 Atomic Physics Q.53P
Give a list of all possible sets of the four quantum numbers (n, ℓ, mℓ, ms) for electrons in the 3p subshell.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics53ps

Chapter 31 Atomic Physics Q.54P
List the values of the four quantum numbers (n, ℓ, mℓ, ms) for each of the electrons in the ground state of magnesium.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics54ps
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Chapter 31 Atomic Physics Q.55P
The configuration of the outer electrons in Ni is 3d8 4s2. Write out the complete electronic configuration for Ni.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics55ps

Chapter 31 Atomic Physics Q.56P
Determine the number of different sets of quantum numbers possible for each of the following shells: (a) n = 2, (b) n = 3, (c) n = 4.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics56ps

Chapter 31 Atomic Physics Q.57P
Generalize the results of Problem 56 and show that the number of different sets of quantum numbers for the n thshell is 2n2.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics57ps
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Chapter 31 Atomic Physics Q.58P
Suppose that the 5d subshell is filled in a certain atom. Write out the 10 sets of four quantum numbers (n, l, ml, ms)for the electrons in this subshell.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics58ps
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Chapter 31 Atomic Physics Q.59P
CE Predict/Explain (a) Tn an X-ray tube, do you expect the wavelength of the characteristic X-rays to increase, decrease, or stay the same if the energy of the electrons striking the target is increased? (b) Choose the liest explanation from among the following:
I. Increasing the energy of the incoming electrons will increase the wavelength of the emitted X-rays.
II. When the energy of the incoming electrons is increased, the energy of the X-rays is also increased; this, in turn, decreases the wavelength.
III. The wavelength of characteristic X-rays depends only on the material used in the metal target, and does not change if the energy of incoming electrons is increased.
Solution:
(a) In an X-ray tube, the wavelength of the characteristic X-rays stays the same if the energy of the electrons striking the target is increased.
(b) The wavelength of characteristic X-rays depends only on the material used in the metal target, and does not change if the energy of incoming electrons is increased.
Therefore option III is the best explanation.

Chapter 31 Atomic Physics Q.60P
CE Is the wavelength of the radiation that excites a fluorescent material greater than, less than, or equal to the wavelength of the radiation the material emits? Explain.
Solution:
The wave length of the radiation that excites a fluorescent material is less than the wavelength of the radiation the material emits.
Explanation:
In fluorescence, a high – frequency photon raises an electron to an excited state. When electron drops back to the ground state, it may do so by way of various intermediate states. The jumps between intermediate states produce photons of lower frequency, which are observed as phenomenon of fluorescence.
The frequency of the radiation that excites a fluorescent material is greater than the frequency of the radiation the material emits. But frequency is inversely proportional to the wavelength.
The wave length of the radiation that excites a fluorescent material is less than the wave length of the radiation the material emits.

Chapter 31 Atomic Physics Q.61P
Using the Bohr model, estimate the wavelength of the Kα X-ray in nickel (Z = 28).
Solution:
mastering-physics-solutions-chapter-31-atomic-physics61ps
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Chapter 31 Atomic Physics Q.62P
Using the Bohr model, estimate the energy of a Kα X-ray emitted by lead (Z = 82).
Solution:
mastering-physics-solutions-chapter-31-atomic-physics62ps

Chapter 31 Atomic Physics Q.63P
The K-shell ionization energy of iron is 8500 eV, and its L-shell ionization energy is 2125 eV. What is the wavelength of Kα X-rays emitted by iron?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics63ps

Chapter 31 Atomic Physics Q.64P
An electron drops from the L shell to the EC shell and gives off an X-ray with a wavelength of 0.0205 nm. What is the atomic number of this atom?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics64ps
mastering-physics-solutions-chapter-31-atomic-physics64ps1

Chapter 31 Atomic Physics Q.65P
Consider an X-ray tube that uses platinum (Z = 78) as its target, (a) Use the Bohr model to estimate the minimum kinetic energy electrons must have in order for Kα X-rays to just appear in the X-ray spectrum of the tube, (b) Assuming the electrons are accelerated from rest through a voltage V, estimate the minimum voltage necessary to produce the KB X-rays.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics65ps

Chapter 31 Atomic Physics Q.66P
BIO Photorefractive Keratectomy A person’s vision may be improved significantly by having the cornea reshaped with a laser beam, in a procedure known as photorefracti ve keratectomy. The excimer laser used in these treatments produces ultraviolet light with a. wavelength of 193 nm. (a) What is the difference in energy between the two levels that participate in stimulated emission in the excimer laser? (b) How many photons from this laser are required to deliver an energy of 1.58 × 10−13 J to the cornea?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics66ps

Chapter 31 Atomic Physics Q.67GP
Consider the following three transitions in a hydrogen atom: (A) ni = 5, nf = 2; (B) ni = 7, nf = 2; (C) ni = 7, nf = 6. Rank the transitions in order of increasing (a) wavelength and (b) frequency of the emitted photon. Indicate ties where appropriate.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics67ps
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Chapter 31 Atomic Physics Q.68GP
Suppose an electron is in the ground state of hydrogen. (a) What is the highest-energy photon this system can absorb without dissociating the electron from the proton? Explain. (b) What is the lowest-energy photon this system can absorb? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics68ps

Chapter 31 Atomic Physics Q.69GP
The electronic configuration of a particular carbon atom is 1s22s22p13s1. Is this atom in its ground state or in an excited state? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics69ps

Chapter 31 Atomic Physics Q.70GP
The electronic configuration of a particular potassium atom is 1s22s22p63s23p63d1. Is this atom in its ground state or in an excited state? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics70ps

Chapter 31 Atomic Physics Q.71GP
Do you expect the ionization energy of sodium (Na) to be greater than, less than, or equal to the ionization energy of lithium (Li)? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics71ps

Chapter 31 Atomic Physics Q.72GP
Find the minimum frequency a photon must have it it is to ionize the ground state of the hydrogen atom.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics72ps

Chapter 31 Atomic Physics Q.73GP
mastering-physics-solutions-chapter-31-atomic-physics73p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics73ps
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Chapter 31 Atomic Physics Q.74GPThe electron in a hydrogen atom makes a transitionfrom the n = 4 state to the n = 2 state, as indicated in R (a) Determine the linear momentum of the photon emitted as a result of this transition, (b) Using your result to part (a), find the recoil speed of the hydrogen atom, assuming it was at rest before the photon was emitted.
mastering-physics-solutions-chapter-31-atomic-physics74p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics74ps
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Chapter 31 Atomic Physics Q.75GP
IP Referring to Problem, find (a) the energy of the emitted photon and (b) the kinetic energy of the hydrogen atom after the photon is emitted. (c) Do you expect the sum of the energies in parts (a) and (b) to be greater than, less than, or the same as the difference in energy between the n = 4 and n = 1 states of hydrogen? Explain.
Problem
74 · · The electron in a hydrogen atom makes a transitionfrom the n = 4 state to the n = 2 state, as indicated in R (a) Determine the linear momentum of the photon emitted as a result of this transition, (b) Using your result to part (a), find the recoil speed of the hydrogen atom, assuming it was at rest before the photon was emitted.
mastering-physics-solutions-chapter-31-atomic-physics75p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics75ps
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Chapter 31 Atomic Physics Q.76GP
BIO Laser Eye Surgery In laser eye surgery, the laser emits a 1.45-ns pulse focused on a spot that is 34.0 μ m in diameter, (a) If the energy contained in the pulse is 2.75 mJ, what is the power per square meter (the irradiance) associated with this beam? (b) Suppose a molecule with a diameter of 0.650 nm is irradiated by the laser beam. How much energy does the molecule receive in one pulse from the laser? (The energy obtained in part (b) is more than enough to dissociate a molecule.)
Solution:
mastering-physics-solutions-chapter-31-atomic-physics76ps
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Chapter 31 Atomic Physics Q.77GP
Consider an electron in the ground-state orbit of the Bohr model of hydrogen. (a) Tind the time required for the electron to complete one orbit about the nucleus. (b) Calculate the current (in amperes) corresponding to the electron’s motion.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics77ps
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Chapter 31 Atomic Physics Q.78GP
A particular Bohr orbit in a hydrogen atom has a total energy of —0.85 eV. What are (a) the kinetic energy of the electron in this orbit and (b) the electric potential energy of the system?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics78ps

Chapter 31 Atomic Physics Q.79GP
The element helium is named for the Sun because that is where it was first observed. (a) What is the shortest wavelength that one would expect to observe from a singly ionized helium atom in the atmosphere of the Sun? (b) Suppose light with a wavelength of 388.9 nm is observed from singly ionized helium. What are the initial and final values of the quantum number n correspondingto this wavelength?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics79ps
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Chapter 31 Atomic Physics Q.80GP
An ionized atom has only a single electron. The n = 6 Bohr orbit of this electron has a radios of 2.72 x 10−10 m. Find (a) the atomic number Z of this atom and (b) the total energy E of its n = 3 Bohr orbit.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics80ps

Chapter 31 Atomic Physics Q.81GP
Find the approximate wavelength of Kβ X-rays emitted by molybdenum (Z = 42), and compare your result with Figure 31–22. (Hint: An electron in the M shell is shielded from the nucleus by the single electron in the K shell, plus all the electrons in the L shell.)
Solution:
mastering-physics-solutions-chapter-31-atomic-physics81ps
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Chapter 31 Atomic Physics Q.82GP
Referring to the hint given in Problem, estimate the wave- ‘ length of La X-rays in molybdenum.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics82ps
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Chapter 31 Atomic Physics Q.83GP
IP The Pickering Series In 1896, the American astronomer Edward C. Pickering (1846–1919) discovered an unusual series of spectral lines in light from the hot star Zeta Puppis. After some time, it was determined that these lines are produced by singly ionized helium. In fact, the “Pickering series” is produced when electrons drop from higher levels to the n = 4 level of He+. Spectral lines in the Pickering series have wavelengths given by
mastering-physics-solutions-chapter-31-atomic-physics83p
In this expression, n = 5,6,7,,… (a) Do you expect the constant C to be greater than, less than, or equal to the Rydberg constant R? Explain. (b) Find the numerical value of C. (c) Pickering lines with n = 6, 8, 10, … correspond to Balmer lines in hydrogen with n = 3, 4, 5, …. Verify this assertion for the n = 6 Pickering line.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics83ps
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Chapter 31 Atomic Physics Q.84GP
IP Rydberg Atoms There is no limit to the size a hydrogen atom can attain, provided it is free from disruptive outside influences. In fact, radio astronomers have detected radiation from large, so-called “Rydberg atoms” inthe diffuse hydrogen gas of interstellar space. (a) Find the smallest value of n such that the Bohr radius of a single hydrogen atom is greater than 8.0 microns, the size of a typical single-celled organism. (b) Find the wavelength of radiation this atom emits when its electron drops from level n to level n −1. (c) If the electron drops one more level, from n − 1 to n − 2,is the emitted wavelength greater than or less than the value found in part (b)? Explain.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics84ps
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mastering-physics-solutions-chapter-31-atomic-physics84ps2

Chapter 31 Atomic Physics Q.85GP
Consider a particle of mass m, charge q, and constant speed v moving perpendicular to a uniformmagnetic field of magnitude B, as shown in Figure. The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the following way: mvr = nh, where n = 1,2,3,…, and h = h/2π.
a. Show that the radii of its allowed orbits have the following values:
mastering-physics-solutions-chapter-31-atomic-physics85p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics85ps
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Chapter 31 Atomic Physics Q.86GP
Consider a particle of mass m confined in a one-dimensional box of length L. In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length L that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the linear momentum of the particle are
mastering-physics-solutions-chapter-31-atomic-physics86p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics86ps
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Chapter 31 Atomic Physics Q.87GP
Show that the time required for an electron in the nth Bohr orbit of hydrogen to circle the nucleus once is given by
mastering-physics-solutions-chapter-31-atomic-physics87p
Solution:
mastering-physics-solutions-chapter-31-atomic-physics87ps

Chapter 31 Atomic Physics Q.88PP
Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts?
A. 1.49 W
B. 5.76 W
C. 5.92 W
D. 6.07 W
Solution:
mastering-physics-solutions-chapter-31-atomic-physics88ps

Chapter 31 Atomic Physics Q.89PP
A different type of laser also emits 1.49 × 1019 photons per second. If all of its photons have a wavelength of 414.0 nm, is its power output greater than, less than, or equal to the power output of the argon laser in Problem?
Problem
88. Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts?
A. 1.49 W
B. 5.76 W
C. 5.92 W
D. 6.07 W
Solution:
mastering-physics-solutions-chapter-31-atomic-physics89ps
mastering-physics-solutions-chapter-31-atomic-physics89ps1

Chapter 31 Atomic Physics Q.90PP
What is the power output of the laser in Problem?
A. 1.23 W
B. 2.39 W
C. 4.80 W
D. 7.16 W
Problem
89. · · A different type of laser also emits 1.49 × 1019 photons per second. If all of its photons have a wavelength of 414.0 nm, is its power output greater than, less than, or equal to the power output of the argon laser in Problem?
Problem
88. Suppose an argon laser emits 1.49 × 1019 photons per second, half with a wavelength of 488.0 nm and half with a wavelength of 514.5 nm. What is the power output of this laser in watts?
A. 1.49 W
B. 5.76 W
C. 5.92 W
D. 6.07 W
Solution:
mastering-physics-solutions-chapter-31-atomic-physics90ps

Chapter 31 Atomic Physics Q.91PP
What is the energy difference (in eV) between the states of an argon atom that are responsible for a photon with a wavelength of 514.5 nm?
A. 2.13 eV
B. 2.42 eV
C. 3.87 eV
D. 6.40 eV
Solution:
mastering-physics-solutions-chapter-31-atomic-physics91ps

Chapter 31 Atomic Physics Q.92IP
IP Referring to Example 31–3 Suppose the electron is in a state whose standing wave consisting of two wavelengths. (a) Is the wavelength of this standing wave greater than or less than 1.33 × 10−9 m? (b) Find the wavelength of this standing wave.
Solution:
mastering-physics-solutions-chapter-31-atomic-physics92ps

Chapter 31 Atomic Physics Q.93IP
Referring to Example 31–3 (a) Which state has a de Broglie wavelength of 3.99 × 10−9 m? (b) Whatis the Bohr radius of this state?
Solution:
mastering-physics-solutions-chapter-31-atomic-physics93ps

Mastering Physics Solutions Chapter 30 Quantum Physics

Mastering Physics Solutions Chapter 30 Quantum Physics

Mastering Physics Solutions

Chapter 30 Quantum Physics Q.1CQ
Give a brief description of the “ultraviolet catastrophe.”
Solution:
mastering-physics-solutions-chapter-30-quantum-physics1cqs

Chapter 30 Quantum Physics Q.1P
CE Predict/Explain The blackbody spectrum of blackbody A peaks at a longer wavelength than that of blackbody B. (a) Is the temperature of blackbody A higher than or lower than the temperature of blackbody B? (b) Choose the best explanation from among the following:

  • Blackbody A has the higher temperature because the higher the temperaturethe longer the wavelength.
  • Blackbody B has the highertemperature because an increase in temperature means an increase in frequency, which corresponds to a decrease in wavelength.

Solution:
mastering-physics-solutions-chapter-30-quantum-physics1ps

Chapter 30 Quantum Physics Q.2CQ
How does Planck’s hypothesis of energy quantization resolve the “ultraviolet catastrophe”?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics2cqs

Chapter 30 Quantum Physics Q.2P
The Surface Temperature of Betelgense Betelgeuse, a red-giant star in the constellation Orion, has a peak in its radiation at a frequency of 1.82 × 1014 Hz. What is the surface temperature of Betelgeuse?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics2ps

Chapter 30 Quantum Physics Q.3CQ
Is there a lowest temperaturebelow which blackbody radiation is no longer given off by an object? Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics3cqs

Chapter 30 Quantum Physics Q.3P
What is the frequency of the most intense radiation emitted by your body? Assume a skin temperature of 95 °F. What is the wavelength of this radiation?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics3ps

Chapter 30 Quantum Physics Q.4CQ
How can an understanding of blackbody radiationallow us to determinethe temperature ofdistant stars?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics4cqs

Chapter 30 Quantum Physics Q.4P
The Cosmic Background Radiation Outer space is filled with a sea of photons, created in the early moments of the universe. The frequency distribution of this “cosmic background radiation” matches that of a blackbody at a temperature near 2.7 K. (a) What is the peak frequency of this radiation? (b) What is the wavelength that corresponds to the peak frequency?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics4ps

Chapter 30 Quantum Physics Q.5CQ
Different Fading Many vehicles inthe United States have a small American flag decal inone of their windows. If the decal has been in place for a long time, the colors will show some
mastering-physics-solutions-chapter-30-quantum-physics5cq
Differential fading, (Conceptual Question 5)
fading from exposure to the Sun. In fact, the red stripes are generally more faded than the blue background for the stars, as shown in the accompanying photo. Photographs and posters react in the same way, with red colors showing the most fading. Explain this effect in terms of the photon model of light.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics5cqs

Chapter 30 Quantum Physics Q.5P
The Sun has a surface temperature of about 5800 K. At what frequency does the Sun emit the most radiation?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics5ps

Chapter 30 Quantum Physics Q.6CQ
Asource of light is monochromatic. What can you say about the photons emitted by this source?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics6cqs

Chapter 30 Quantum Physics Q.6P
(a) By what factor does the peak frequency change if the Kelvin tempera ture of an object is doubled from 20.0 K to 40.0 K? (b) By what factor does the peak frequency change if the Celsius temperature of an object is doubled from 20.0 °C to 40.0 °C?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics6ps
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mastering-physics-solutions-chapter-30-quantum-physics6ps2

Chapter 30 Quantum Physics Q.7CQ
The relative Intensity of radiation, given off by a blackbody is shown in Figure 30–2. Notice that curves corresponding to different temperatures never cross one another. If two such curves did intersect, however, it would be possible to violate the second law of thermodynamics. Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics7cqs

Chapter 30 Quantum Physics Q.7P
IP A Famous Double Star Albireo in the constellation Cygnus, which appears as a single star to the naked eye, is actually a beautiful double-star system. The brighter of the two stars is referred to as A (or Beta-01 Cygni), with a surface tempera ture of TA = 4700 K; its companion is B (or Beta-02 Cygni), with a surface temperature of TB = 13,000 K. (a) When viewed througha telescope, one star is a brilliant blue color, and the other has a warm golden color, as shown in the accompanying photo. Is the blue star A or B? Explain, (b) What is the ratio of the peak frequencies emitted by the two stars, (fA/fB)?
mastering-physics-solutions-chapter-30-quantum-physics7p
Solution:
mastering-physics-solutions-chapter-30-quantum-physics7ps
=0.3615

Chapter 30 Quantum Physics Q.8CQ
(a) Is it possible for a photon from a green source of light to have more energy than a photon from a blue source of light? Explain, (b) Is it possible for a photon from a green source oflight to have more energy than a photon from a red source of light? Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics8cqs

Chapter 30 Quantum Physics Q.8P
IP Halogen Lightbulbs Modern halogen lightbulbs allow their filaments to operate at a highertemperature than the filaments in standard Incandescent bulbs. For comparison, the filament in a standard lightbulb operates at about 2900 K, whereas the filament ina halogen bulb may operate at 3400 K.
(a) Which bulb has the higher peak frequency? (b) Calculate the ratio of peak frequencies (f hal/f std). (c) The humaneye is most sensitive to a frequency around 5.5 × 1014 Hz. Which bulb produces a peak frequency closer to this value?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics8ps
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Chapter 30 Quantum Physics Q.9CQ
Light of a given wavelength ejects electrons from the surfaceof one metal but not from the surface of another metal. Give a possible explanation for this observation.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics9cqs

Chapter 30 Quantum Physics Q.9P
IP A typical lightbulb contains a tungsten filament that reaches a temperature of about 2850 K, roughly half the surface temperatureof the Sun. (a) Treating the filament as a blackbody, determine the frequency for which its radiation is a maximum. (b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics9ps
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Chapter 30 Quantum Physics Q.10CQ
Why does the existence of a cutoff frequency inthe photoelectric effect argue in favor of the photon model of light?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics10cqs

Chapter 30 Quantum Physics Q.10P
Exciting au Oxygen Molecule An oxygen molecule (O2) vibrates with an energy identical to that of a single particle of mass m = 1.340 × 10−26 kg attached to a spring with a force constant of k = 1215 N/m. The energy levels of the system are uniformly spaced, as indicated in Figure 20, with a separation given by hf. (a) What is the vibration frequency of this molecule? (b) How much energy must be added to the molecule to excite it from one energy level to the next higher level?
mastering-physics-solutions-chapter-30-quantum-physics10p
Solution:
mastering-physics-solutions-chapter-30-quantum-physics10ps
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Chapter 30 Quantum Physics Q.11CQ
Why can an electron microscope resolve, smaller objects than a light microscope?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics11cqs

Chapter 30 Quantum Physics Q.11P
CE source of red light, a source of green light, and a source of blue light each produce beams of light with the same power. Rank these sources in order of increasing (a) wavelength of light, (b) frequency of light, and (c) number of photons emitted per second. Indicate ties where appropriate.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics11ps
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Chapter 30 Quantum Physics Q.12CQ
A proton is about 2000 times more massive than an electron. Is it possible for an electron to have the same de Broglie wavelength as a proton? Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics12cqs
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Chapter 30 Quantum Physics Q.12P
CE Predict/Explain A source of red light has a higher-wattage than a source of green light. (a) Is the energy of photons emitted by the red source greater than, less than, or equal to the energy of photons emitted by the green source? (b) Choose the best explanation from among the following:
I. The photons emitted by the red source have the greater energy because that source has the greater wattage.
II. The red-source photons have less energy than the green-source photons because they have a lower frequency. The wattage of the source doesn’t matter.
III. Photons from the red source have a lower frequency, but that source also has a greater wattage. The two effects cancel, so the photons have equal energy.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics12ps

Chapter 30 Quantum Physics Q.13P
CE Predict/Explain A source of yellow light has a higher-wattage than a source of blue light. (a) Is the number of photons emitted per second by the yellow source greater than, less than, or equal to the number of photons emitted per second by the blue source? (b) Choose the test explanation from among the following:

  • The yellow source emits more photons per second because
    • it emits more energy per second than the blue source, and
    • its photons have less energy than those of the blue source.
  • The yellow source has the higher wattage, which means its photons have higher energy than the blue-source photons. Therefore, the yellow source emits fewer photons per second.
  • The two sources emit the same number of photons per second because the higher wattage of the yellow source compensates for the higher energy of the blue photons.

Solution:
mastering-physics-solutions-chapter-30-quantum-physics13ps

Chapter 30 Quantum Physics Q.14P
CE Predict/Explain Light of a particular wavelength does not eject electrons from the surface of a given metal, (a) Should the wavelength of the light be increased or decreased in order to cause electrons to be ejected? (b) Choose the best explanation from among the following:

  • The photons have too little energy to eject electrons. To increase their energy, their wavelength should be Increased.
  • The energy of a photon is proportional to its frequency; that is, inversely proportional to its wavelength. To increase the energy of the photons so they can eject electrons, one must decrease their wavelength.

Solution:
mastering-physics-solutions-chapter-30-quantum-physics14ps

Chapter 30 Quantum Physics Q.15P
CE Light of a particular wavelength and intensity does not eject efectrons from the surface of a given metal. Can electrons be ejected from the metal by increasing the intensity of the light? Explain.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics15ps

Chapter 30 Quantum Physics Q.16P
When a person visits the local tanning salon, they absorb photons of ultraviolet (UV) light to get the desired tan. What are the frequency and wavelength of a LJV photon whose energy is 6.5 × 10−19 J?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics16ps

Chapter 30 Quantum Physics Q.17P
An AM radio station operating at a frequency of 880 kHz radiates 270 kW of power from its antenna. How many photons are emitted by the antenna every second?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics17ps

Chapter 30 Quantum Physics Q.18P
Aphoton with a wavelength of less than 50.4 ran can ionize a helium atom. What is the ionization potential of helium?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics18ps

Chapter 30 Quantum Physics Q.19P
Aflashlight emits 2.5 W of light energy. Assuming a frequency of 5.2 × 1014 Hz for the light, determine the number of photons given off by the flashlight per second.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics19ps

Chapter 30 Quantum Physics Q.20P
Light of frequency 9.95 × 1014 Hz ejects electrons from the surface of silver. If the maximum kinetic energy of the ejected electrons is 0.180 × 10−19 J, what is the work function of silver?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics20ps

Chapter 30 Quantum Physics Q.21P
The work function of gold is 4.58 eV. What frequency of light must be used to eject electrons from a gold surface with a maximum kinetic energy of 6.48 × 10−19 J?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics21ps

Chapter 30 Quantum Physics Q.22P
(a) How many 350-nm (UV) photons- are needed to provide a total energy of 2.5 J? (b) How many 750-nm (red) photons are needed to provide the same energy?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics22ps

Chapter 30 Quantum Physics Q.23P
(a) Mow many photons per second are emitted by a monochromatic lightbulb (λ = 650 nm) that emits 45 W of power? (b) If you stand 15 m from this bulb, how many photons enter each of your eyes per second? Assume your pupil is 5.0 mm in diameter and that the bulb radiates uniformly in all directions.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics23ps
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Chapter 30 Quantum Physics Q.24P
IP Two 57.5-kW radio stations broadcast at different frequencies. Station A broadcasts ata frequency of 892 kHz, and station B broadcasts at a frequency of 1410 kHz. (a) Which station emits more photons per second? Explain, (b) Which station emits photons of higher energy?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics24ps

Chapter 30 Quantum Physics Q.25P
Dissociating the Hydrogen Molecule The energy required to separate a hydrogen molecule into its individual atoms is 104.2 kcal per mole of H2. (a) If the dissociation energy for a single H2 molecule is provided by one photon, determine its frequency and wavelength. (b) In what region of the electromagnetic spectrum does the photon found in part (a) lie? (Refer to the spectrum shown in Figure 25–8.)
Solution:
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Chapter 30 Quantum Physics Q.26P
(a) How many photons are emitted per second by a He-Ne laser that emits 1.0 mW of power at a wavelength λ = 632.8 nm? (b) What is the frequency of the electromagnetic waves emitted by a He-Ne laser?
Solution:
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Chapter 30 Quantum Physics Q.27P
IP You have two lightbulbs of different power and color, as indicated in Figure30-21. One is a 150-W red bulb, and the other is a 25-W blue bulb. (a) Which bulb emits more photons per second? (b) Which bulb emits photons of higher energy? (c) Calculate the number of photons emitted per second by each bulb. Take λred = 650 nm and λb1ue = 460 nm. (Most of the electromagnetic radiation given off by incandescent lightbulbs is in
mastering-physics-solutions-chapter-30-quantum-physics27p
FIGURE 10–11 Problem 27
the infrared portion of the spectrum. For the purposes of trug problem, however, assume that all of the radiated power is at the wavelengths indicated.)
Solution:
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Chapter 30 Quantum Physics Q.28P
The maximum wavelength an electromagnetic wave can have and still eject an electron from a copper surface is 264 nm. What is the work functionof a copper surface?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics28ps

Chapter 30 Quantum Physics Q.29P
IP Aluminum and calcium have photoelectric work functions of WAI = 4.28 eV and WCa, = 2.87 eV, respectively, (a) Which metal requireshigher-frequency light to produce photoelectrons? Explain, (b) Calculate the minimum frequency that will produce photoelectrons from each surface.
Solution:
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Chapter 30 Quantum Physics Q.30P
IP Two beams of light with different wavelengths (λA > λB) are used to produce photoelectrons from a given metal surface, (a) Which beam produces photoelectrons with greater kinetic energy? Explain, (b) Find Kmax for cesium (W0 = 1.9 eV) if λA = 620 nm and λB = 410 nm.
Solution:
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Chapter 30 Quantum Physics Q.31P
IP Zinc and cadmium have photoelectric work functions given by WZn = 4.33 eV and WCd = 4.22 cV, respectively, (a) If both metals are illuminated by UV radiation of the same wavelength, whichone gives off photoelcctrons with the greater maximum kinetic energy? Explain, (b) Calculate the maximum kinetic energy of photoelectrons from each surface if λ = 275 nm.
Solution:
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Chapter 30 Quantum Physics Q.32P
White light, with frequencies ranging from 4.00 × 1014 Hz to 7.90 × 1014 Hz, is incident on a potassium surface. Given tha t the work function of potassium is 2.24 eV, find (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.
Solution:
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Chapter 30 Quantum Physics Q.33P
Electromagnetic waves, with frequencies ranging from 4.00 × 1014 Hz to 9.00 × 1016 Hz, are incident on an aluminum surface. Given that the work function of aluminum is 4.28 eV, find (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.
Solution:
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Chapter 30 Quantum Physics Q.34P
IP Platinum has a work function of 6.35 eV, and iron has a work function of 4.50 eV. Light of frequency 1.88 × 1015 Hz ejects electrons from both of these surfaces, (a) From which surface will the ejected electrons have a greater maximum kinetic energy? Explain, (b) Calculate the maximum kinetic energy of ejected electrons for each surface.
Solution:
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Chapter 30 Quantum Physics Q.35P
When light with a frequency f1 = 547.5 THz illuminates a metal surface, the most energetic photoelectrons have 1.260 × 10−19 J of kinetic energy. When light with a frequency f2 = 738.8THz is used Instead, the most energetic photoelectrons have 2.480 × 10−19 J of kinetic energy. Using these experimental results, determine the approximate value of Planck’s constant.
Solution:
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Chapter 30 Quantum Physics Q.36P
BIO Owl Vision Owls have large, sensitive eyes for good night vision. Typically, the pupil of an owl’s eye can have a diameter of 8.5 mm (as compared with a maximum diameter of about 7.0 mm for humans). In addition, an owl’s eye is about 100
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Solution:
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Chapter 30 Quantum Physics Q.37P
CE If the momentum of a particle with finite mass is doubled, its kinetic energy increases by a factor of 4. If the momentum of a photon is doubled, by what factor does its energy increase?
Solution:
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Chapter 30 Quantum Physics Q.38P
The photons used in microwave ovens have a momentum of 5.1 × 10−33 kg· m/s.(a) What is their wavelength? (b) How does the wavelength of the microwaves compare with the size of the holes in the metal screen on the door of the oven?
Solution:
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Chapter 30 Quantum Physics Q.39P
What speed must an electron have if its momentum is to be the same as that of an X-ray photon with a wavelength of· 0.25 nm?
Solution:
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Chapter 30 Quantum Physics Q.40P
What is the wavelength of a photon that has the same momentum as an electron moving with a speed of 1200 m/s?
Solution:
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Chapter 30 Quantum Physics Q.41P
What is the frequency of a photon that has the same momentum as a neutron moving with a speed of 1500 m/s?
Solution:
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Chapter 30 Quantum Physics Q.42P
A hydrogen atom, initially at rest, emits an ultraviolet photon with a wavelength ofλ = 122 nm. What is the recoil speed of the atom after emitting the photon?
Solution:
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Chapter 30 Quantum Physics Q.43P
A blue-green photon (λ = 486 nm) is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen atom after absorbing the photon?
Solution:
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Chapter 30 Quantum Physics Q.44P
IP (a) Which has the greater momentum, a photon of red light or a photon of blue light? Explain. (b) Calculate the momentum of a photon of red light (f = 4.0 × 1034 Hz) and a photon of blue light (f = 7.9 × 1014 Hz).
Solution:
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Chapter 30 Quantum Physics Q.45P
IP Photon Ahas twice the momentum of photon B. (a) Which photon has the greaterwavelength? Explain, (b) If the wavelength of photon A is 333 nm, what is the wavelength of photon B?
Solution:
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Chapter 30 Quantum Physics Q.46P
A laser produces a 5.00-mW beam of light, consisting of photons with a wavelength of 632.8 run. (a) How many photons are emitted by the laser each second? (b) The laser beam strikes a black surface and is absorbed. What is the change in the momentum of each photon that is absorbed? (c) What force does the laser beam exert on the bJack surface?
Solution:
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Chapter 30 Quantum Physics Q.47P
A Jaser produces a 7.50-mW beam of light, consisting of photons with a wavelength of 632.8 nm. (a) How many photons are emitted by the laser each second? (b) The laser beam strikes a mirror at normal incidence and is reflected. What is the change in momentum of each reflected photon? Give the magnitude only, (c) What force does the laser beam exert on the mirror?
Solution:
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Chapter 30 Quantum Physics Q.48P
CE In a Compton scattering experiment, the scattered elec tron is observed to move in the same direction as the incident X-ray photon. What is the scattering angle of the photon? Explain.
Solution:
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Chapter 30 Quantum Physics Q.49P
An X-ray photon has 38.0 keV of energy before it scatters from a free electron, and 33.5 keV after it scatters. What is the kinetic energy of the recoiling electron?
Solution:
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Chapter 30 Quantum Physics Q.50P
In the Compton effect, an X-ray photon scatters from a free electron. Find the change in the photon’s wavelength if it scatters at an angle of (a) θ = 30.0°, (b) θ = 90.0°, and (c) θ = 180.0” relative to the incident direction.
Solution:
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Chapter 30 Quantum Physics Q.51P
An X-ray scattering from a free electron is observed to change its wavelength by 3.13 pm. At what angle to the incident direction does the scattered X-ray move?
Solution:
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Chapter 30 Quantum Physics Q.52P
The maximum Compton shift in wavelength occurs when a photon is scattered through 180°. What scattering angle will produce a wavelength shift of one-fourth the maximum?
Solution:
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Chapter 30 Quantum Physics Q.53P
Consider two different photons that scatter through an angle of 180° from a free electron. One is a visible-light photon with λ = 520 nm, the other is an X-ray photon with λ = 0.030 nm. (a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain. (b) Which photon experiences the greater percentage change in wavelength? Explain. (c) Calculate the percentage change in wavelength of each photon.
Solution:
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Chapter 30 Quantum Physics Q.54P
An X-ray photon with a wavelength of 0.240 nm scatters from a free electron at rest. The scattered photon moves at an angle of 105° relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.
Solution:
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Chapter 30 Quantum Physics Q.55P
An X-ray photon scatters from a free electron at rest at an angle of 175° relative to the incident direction. (a) If the scattered photon has a wavelength of 0.320 nm, what is the wavelength of the incident photon? (b) Determine the energy of the incident and scattered photons. (c) Find the kinetic energy of the recoil electron.
Solution:
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Chapter 30 Quantum Physics Q.56P
An X-ray photon scatters through 180° from (i) an electron or (ii) a helium atom. (a) In which case is the change in wavelength of the X-ray greater? Explain. (b) Calculate the change in wavelength for each of these two cases.
Solution:
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Chapter 30 Quantum Physics Q.57P
A photon has an energy E and wavelength λ before scattering from a free electron. After scattering through a 135° angle, the photon’s wavelength has increased by 10.0%. Find the initial wavelength and energy of the photon.
Solution:
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Chapter 30 Quantum Physics Q.58P
Find the direction of propagation of the scattered electron in Problem 51, given that the incident X-ray has a wavelength of 0.525 nm and propagates in the positive x direction.
Problem
An X-ray scattering from a free electron is observed to change its wavelength by 3.13 pm. At what angle to the incident direction does the scattered X-ray move?
Solution:
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Chapter 30 Quantum Physics Q.59P
Predict/Explain (a) As you accelerate your car away from a stoplight, does the de Broglie wavelength of the car increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The de Broglie wavelength will increase because the momentum of the car has increased.
II. The momentum of the car increases. It follows that the de Broglie wavelength will decrease, because it is inversely proportional to the wavelength.
III. The de Broglie wavelength of the car depends only on its mass, which doesn’t change by pulling away from the stoplight. Therefore, the de Broglie wavelength stays the same.
Solution:
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Chapter 30 Quantum Physics Q.60P
By what factor does the de Broglie wavelength of a particle change if (a) its momentum is doubled or (b) its kinetic energy is doubled? Assume the particle is nonrelativistic.
Solution:
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Chapter 30 Quantum Physics Q.61P
A particle with a mass of 6.69 × 10–27 kg has a de Broglie wavelength of 7.22 pm. What is the particle’s speed?
Solution:
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Chapter 30 Quantum Physics Q.62P
What speed must a neutron have if its de Broglie wavelength is to be equal to the interionic spacing of table salt (0.282 nm)?
Solution:
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Chapter 30 Quantum Physics Q.63P
A 79-kg jogger runs with a speed of 4.2 m/s. If the jogger is considered to be a particle, what is her de Broglie wavelength?
Solution:
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Chapter 30 Quantum Physics Q.64P
Find the kinetic energy of an electron whose de Broglie wavelength is 1.5 Å
Solution:
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Chapter 30 Quantum Physics Q.65P
A beam of neutrons with a de Brogue M’a velength of 0.250 nn diffracts from a crystal of table salt, which has an interionic spacing of 0.282 nm. (a) What is the speed of the neutrons? (b) What is the angle of the second interference maximum?
Solution:
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Chapter 30 Quantum Physics Q.66P
IP An electron and a proton have the same speed, (a) Which has the longer de Broglie wavelength? Explain. (b) Calculate the ratio (λe/λp).
Solution:
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Chapter 30 Quantum Physics Q.67P
IP An electron and a proton have the same de Broglie wavelength, (a) Which has the greater kinetic energy? Explain. (b) Calculatethe ratio of the electron’s kinetic energy to the kinetic energy of the proton.
Solution:
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Chapter 30 Quantum Physics Q.68P
Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted, (a) At what speed will the de Broglie wavelength of a 65-kg student be equal to the 0.76-m width of a doorway? (b) At this speed, how long will it take the student to travel a distance of 1.0 mm? (For comparison, the age of the universe is approximately 4 × 1017s.)
Solution:
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Chapter 30 Quantum Physics Q.69P
A particle has a mass m and an electric charge q. The particle is accelerated from rest through a potential difference V. What is the particle’s de Broglie wavelength, expressed in terms of m, q, and V?
Solution:
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Chapter 30 Quantum Physics Q.70P
A baseball (0.15 kg) and an electron both have a speed of 41 m/s. Find the uncertainty in position of each of these objects, given that the uncertainty in their speed is 5.0%.
Solution:
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Chapter 30 Quantum Physics Q.71P
The uncertainty in position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus, If this diameter is 7.5 × 10−15, what is the uncertainty in the proton’s momentum?
Solution:
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Chapter 30 Quantum Physics Q.72P
“ The position of a 0.26-kg air-track cart is determined to within an uncertainty of 2.2 nun. What speed must the cart acquire as a result of the position measurement?
Solution:
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Chapter 30 Quantum Physics Q.73P
The measurement of an electron’s energy requires a time interval of 1.0 × 10–8 s. What is the smallest possible uncertainty in the electron’s energy?
Solution:
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Chapter 30 Quantum Physics Q.74P
A particle’s energy is measured with an uncertainty of 0.0010 eV. What is the smallest possible uncertainty in our knowledge of when the particle had this energy?
Solution:
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Chapter 30 Quantum Physics Q.75P
An excited state of a particular atom has a mean lifetime of 0.60 × 10–9 s, which we may take as the uncertainty Δt. What is the minimum uncertainty in any measurement of the energy of this state?
Solution:
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Chapter 30 Quantum Physics Q.76P
The ∑+ is an unstable particle, with a mean lifetime of 2.5 × 10–10 s. Its lifetime defines the uncertainty ∆t for this particle. What is the minimum uncertainty in this particle’s energy?
Solution:
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Chapter 30 Quantum Physics Q.77P
The uncertainty in an electron’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty (∆p = p)?
Solution:
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Chapter 30 Quantum Physics Q.78P
The uncertainty in a proton’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of a proton whose momentum is equal to this uncertainty (∆p = p)?
Solution:
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Chapter 30 Quantum Physics Q.79P
An electron has a momentum p ≈ 1.7 × 10–25kg · m/s. What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum (∆p/p) below 1.0%?
Solution:
The Heisenberg’s uncertainty principle in terms of momentum and position is,
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Chapter 30 Quantum Physics Q.80GP
CE Suppose youperform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the intensity of the light is increased while the frequency is held constant, describe whether the following quantities increase,, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.
Solution:
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Chapter 30 Quantum Physics Q.81GP
CE Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increase, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.
Solution:
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Chapter 30 Quantum Physics Q.82GP
CE An electron that is accelerated from rest through a potential difference V0 has a de Broglie wavelength λ0. What potential difference will double the electron’s wavelength? (Express your answer in terms of V0.)
Solution:
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Chapter 30 Quantum Physics Q.83GP
CE A beam of particles diffracts from a crystal, producing an interference maximum at the angle θ. (a) If the mass of the particles is increased, with every thing else remainingthe same, does the angle of the interference maximum increase, decrease, or stay the same? Explain (b). If the energy of the particles is increased, with every tiling else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain.
Solution:
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Chapter 30 Quantum Physics Q.84GP
You want to construct a photocell that works with visible light. Three materials are readily available: aluminum (W0 = 4.28 eV), lead (W0 = 4.25 eV), and cesium (W0 = 2.14 eV). Which materials) would be suitable?
Solution:
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Chapter 30 Quantum Physics Q.85GP
BIO Human Vision Studies have shown that some people can detect 545-nm light with as few as 100 photons entering the eye per second. Wha t is the power delivered by such a beam of light?
Solution:
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Chapter 30 Quantum Physics Q.86GP
A pendulum consisting of a 0.15-kg mass attached to a 0.78-m string undergoes simple harmonic motion, (a) What is the frequency of oscillation for this pendulum? (b) Assuming the energy of this system satisfies En = nhf, find the maximum speed of the 0.15-kg mass when the quantum number is 1.0 × 1033.
Solution:
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Chapter 30 Quantum Physics Q.87GP
To listen to a radio station, a certain home receiver must pick up a signal of at least 1.0 × 10−10 W. (a) If the radio waves have a frequency of 96 MHz, how many photons must the receiver absorb per second to get the station? (b) How much force is exerted on the receiving antenna for the case considered in part (a)?
Solution:
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Chapter 30 Quantum Physics Q.88GP
The latent heat for converting ice at0°C to water at 0°C is 80.0 kcal/kg (Chapter 17). (a.) How many photons of frequency 6.0 × 101.1 Hz must be absorbed by a 1.0-kg block of ice at 0 °C to melt it to water at 0 °C? (b) How many molecules of H2O can one photon convert from ice to water?
Solution:
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Chapter 30 Quantum Physics Q.89GP
How many 550-nm photons would have to be absorbed to raise the temperature of 1.0 g of water by 1.0 C°?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics89ps

Chapter 30 Quantum Physics Q.90GP
A microwave oven can heat 205 ml of water from 20.0 °C to 90.0 °C in 2.00 min. If the wavelength of the microwaves is λ= 12.2 cm, how many photons were absorbed by the water? (Assume no loss of heat by the water.)
Solution:
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Chapter 30 Quantum Physics Q.91GP
Light with a frequency of 2.11 × 1015 Hz ejects electrons from the surface of lead, which has a work function of 4.25 eV. What is the minimum de Broglie wavelength of the ejected electrons?
Solution:
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Chapter 30 Quantum Physics Q.92GP
An electron moving with a speed of 2.7 × 106 m/s has the same momentum as a photon. Find (a) the de Broglie wavelength of the electron and (b) the wavelength of the photon.
Solution:
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Chapter 30 Quantum Physics Q.93GP
BIO The Cold Light of Fireflies Fireflies are often said to give off “cold light.” Given that the peak ina firefly’s radiation occurs at about 5.4 × 1014 Hz, determine the temperature of a blackbody that would have the same peak frequency. From your result, would you say that firefly radiation is well approximated by blackbody radiation? Explain.
Solution:
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Chapter 30 Quantum Physics Q.94GP
IP When light with a wavelength of 545 runshines on a metal surface, electrons are ejected with speeds of 3.10 × 105 m/s or less. (a) Give a strategythat allows you to use the preceding information to calculate the work function and cutoff frequency for this surface. (b) Carry out your strategy and determine the work function and cutoff frequency.
Solution:
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Chapter 30 Quantum Physics Q.95GP
IP A hydrogen atom absorbs a 486.2-nrn photon. A short time later, the same atom emits a photon with a wavelength of 97.23 nm. (a) Has the net energy of the atom increased or decreased? Explain. (b) Calculate the change in energy of the hydrogen atom.
Solution:
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Chapter 30 Quantum Physics Q.96GP
When a beam of atoms emerges from an oven at the absolute temperature T, the most probable de Broglie wavelength for a given atom is
mastering-physics-solutions-chapter-30-quantum-physics96p
In this expression, m is the mass of an atom, and k is Boltz-mann’s constant (Chapter). What is the most probable speed of a hydrogen atom emerging from an oven at 450 K?
Solution:
mastering-physics-solutions-chapter-30-quantum-physics96ps
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Chapter 30 Quantum Physics Q.97GP
mastering-physics-solutions-chapter-30-quantum-physics97p
Solution:
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Chapter 30 Quantum Physics Q.98GP
A jar is filled with monatomic helium gas at a temperature of 25 °C. The pressure inside the jar is one atmosphere; that is, 101 kPa. (a) Find the average de Broglie wavelength of the he-Hum atoms. (b) Calculate the average separation between helium atoms in the jar. (Note: The fact that the spacing between atoms is much greater than the de Broglie wavelength means quantumeffects are negligible, and the atoms can be treated as particles.)
Solution:
mastering-physics-solutions-chapter-30-quantum-physics98ps
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Chapter 30 Quantum Physics Q.99GP
The Compton Wavelength The Compton wavelength, λC, of a particle of mass m is defined as follows: λC = h/mc. (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part
(a), (c) Show, in general, that a photon with a “wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics99ps
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Chapter 30 Quantum Physics Q.100GP
IP Light of frequency 8.22 × 1014 Hz ejects electrons from surface A with a maximum kinetic energy that is 2.00 × 10−19 J greater than the maximum kinetic energy of electrons ejected from surface B. (a) If the frequency of the light is increased, does the difference in maximum kinetic energy observed from, the two surfaces increase, decrease, or stay the same? Explain. (b) Calculate the difference in work function for these two surfaces.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics100ps
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Chapter 30 Quantum Physics Q.101PP
What is the work function, W0, for lithium, as determined from Millikan’s results?
A. 0.0112 eV
B. 0.951 eV
C. 1.63 eV
D. 2.29 eV
Solution:
mastering-physics-solutions-chapter-30-quantum-physics101ps
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Chapter 30 Quantum Physics Q.102PP
What value does Millikan obtain for Planck’s constant, based on the lithium measurements? (His value is close to, but not the same as, the currently accepted value.)
A. 1.12 × 10−34 J· s
B. 3.84 × 10−34 J· s
C. 6.14 × 10−34 J· s
D. 6.57 × 10−34 J· s
Solution:
mastering-physics-solutions-chapter-30-quantum-physics102ps
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Chapter 30 Quantum Physics Q.103PP
What maximum kinetic energy do you predict Millikan found when he used light with a wavelength of 365.0 nm?
A. 0.805 eV
B. 1.08 eV
C. 2.29 eV
D. 2.82 eV
Solution:
mastering-physics-solutions-chapter-30-quantum-physics103ps

Chapter 30 Quantum Physics Q.104IP
IP Referring to Example 30–4 An X-ray photon with λ = 0.6500 nm scatters from an electron, giving the electron a kinetic energy of 7.750 eV. (a) Is the scattering angle of the photon greater than, less than, or equal to 152°? (b) Find the scattering angle.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics104ps
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Chapter 30 Quantum Physics Q.105IP
IP Referring to Example 30–4 An X-ray photon with λ = 0.6500 nm scatters from an electron. The wavelength of the scattered photon is 0.6510 nm. (a) Is the scattering angle in this case greater than, less than, or equal to 152°? (b) Find the scattering angle.
Solution:
mastering-physics-solutions-chapter-30-quantum-physics105ps

Mastering Physics Solutions Chapter 29 Relativity

Mastering Physics Solutions Chapter 29 Relativity

Mastering Physics Solutions

Chapter 29 Relativity Q.1CQ
Some distant galaxies are moving away from us at speeds greater than 0.5c. What is the speed of the light received on Earth from these galaxies? Explain.
Solution:
According to second postulate of special theory of relativity the speed of light (c) is same in all inertial frames of references in vacuum. So light from these galaxies received on the earth moves with the speed as is true for all light in a vacuum.

Chapter 29 Relativity Q.1P
CE Predict/Explain You are in spaceship, traveling directly away from the Moon with a speed of 0.9c A light signal is sent in your direction from the surface of the Moon. (a) As the signal passes your ship, do you measure its speed to be greater than, among the following:

  • the speed you measure will be greater then 0.1c in fact, it will be c, since all observers in inertial frames measure the same speed of light
  • You will measure a speed less than 0.1c because of time dilation, which causes clocks to run slow.
  • When you measure a speed you find if be between c and 0.9c.

Solution:

  • As the signal passes our ship, we will measure speed of the signal greater than 0.1c
  • Answer (I) The speed you measure will be greater than 0.1c; in fact, it will be c, since all observers in inertial frames measures the same speed of light.

Chapter 29 Relativity Q.2CQ
The speed of light in glass is less than c. Why is this not a violation of the second postulate of relativity?
Solution:
We know according to second postulate of special theory of relativity, the speed (c) of light is same in all inertial frames of references, and speed of light in vacuum is c. Here c is the speed of light in vacuum only. In all other media other than vacuum the speed of light is less than c. So the speed of light in glass is less than c.

Chapter 29 Relativity Q.2P
Albert is piloting his spaceship, heading east with a speed of 0.90c. Albert’s ship sends a light beam in the forward (east-ward) direction, which travels away from his ship at a speed c. Meanwhile, Isaac is piloting his ship in the westward direction, also at 0.90c, toward Albert’s ship. With what speed does Isaac see?
Solution:
According to second postulate of special theory of relativity, the speed of light in vacuum, , is same in all inertial frames of reference, independent of the motion of the source or the receiver. The speed of Albert’s light beam observed by Isaac is c

Chapter 29 Relativity Q.3CQ
How would velocities add if the speed of light were infinitely large? Justify your answer by considering Equation 29–4.
Solution:
mastering-physics-solutions-chapter-29-relativity3cqs

Chapter 29 Relativity Q.3P
CE A street performer tosses a ball straight up into the air (event 1) and then catches it in his mouth (event 2). For each of the following observers, state whether the time they measure between these two events is the proper time or the dilated time: (a) the street performer; (b) a stationary observer on the other side of the street; (c) a person sitting at home watching the performance on TV; (d) a person observing the performance from a moving car.
Solution:
The definition of proper time is the time difference between the two events which occur at the same location by given observer or particular observer. Here in the given problem, the two events are a street performer tosses a ball straight up into the air (event 1) and then catches it in his mouth (event 2). Now we have to decide for the following observers, whether the time they measured between these two events is the proper time or dilated time.

  • (a) Here the street performer is in the rest frame of reference. With respect to this street performer these two events occur at the same location. So he measures the time between these two events is proper time
  • (b) The stationary observer on the other side of the street is also in the rest frame. With respect to him these two events occur at the same location. So he measures the time between these two events is proper time
  • (c) The person sitting at home watching the performance on TV is in the rest frame. With respect to him these two events occur at the same location. So he measures the time difference between these two events is proper time
  • (d) A person moving in the car observed these two events are situated at different locations. So with respect to him, he measures the time between these two events is dilated time

Chapter 29 Relativity Q.4CQ
Describe some of the everyday consequences that would follow if the speed of light were 35 mi/h.
Solution:
If the speed of light is 35 mi/h then we experience relativistic effects like

  •  A person in motion would age slowly than a person who stays at home due to time dilation.
  •  The length of a car in motion seems to be shorter due to length contraction.
  •  No object can move faster than light.

Even if the engine of your car is very powerful and even if you try to accelerate it, your car will not be able to move faster than 35 mi/h

Chapter 29 Relativity Q.4P
СE Predict/Explain A clock in a moving rocket is observed to run slow, (a) If the rocket reverses direction, does the clock run slow, fast, or at its normal rate? (b) Choose the best explanation from among the following:

  • The clock will run slow, just as before. The rate of the clock depends only on relative speed, not on direction of motion.
  • When the rocket reverses direction the rate of the clock reverses too, and this makes it run fast.
  • Reversing the direction of the rocket undoes the the time dilation effect, and so the clock will now run at its normal rate.

Solution:

  • The clock will still run slow as before.
  • Answer (I)

The clock will run slow, just as before. The rate of the clock depends only on relative speed, not on direction of motion.

Chapter 29 Relativity Q.5CQ
When we view a distant galaxy, we notice that the light coming from it has a longer wavelength (it is “red-shifted”) than the corresponding light here on Earth. Is this consistent with the postulate that all observers measure the same speed of light? Explain.
Solution:
Yes
Here the light rays are coming from the distant galaxy. In spite of not taking the wavelength of the light rays coming from the galaxy, all these light rays move with the same speed in vacuum. These light rays have longer wavelength and the frequency of this “red shifted” light will be affected, this is because we know the formula. v = λf From this formula the wavelength () and frequency (f) of the light rays are inversely proportional to each other. From this relation the longer wavelength implies a smaller frequency.

Chapter 29 Relativity Q.5P
СE Predict/Explain Suppose you are a traveling salesman for SSC, the Spacely Sprockets Company. You travel on a spaceship that reaches speeds near the speed of light, and you are paid by the hour, (a) When you return to Earth after a sales trip, would you prefer to be paid according to the clock at Spacely Sprockets universal headquarters on Earth, according to the clock on the spaceship in which you travel, or would your pay be the same in either case? (b) Choose the best explanation from among the following:

  • You want to be paid according to the clock on Earth, because the clock on the spaceship runs slow when it approaches the speed of light.
  • Collect your pay according to the clock on the spaceship because according to you the clock on Earth has run slow.
  • Your pay would be the same in either case because motion is relative, and all mertial observers will agree on the amount of time that has elapsed.

Solution:

  • I would like to be paid according to the clock at Spacely Sprockets universal Headquarters on earth.
  • Answer (I) You want to be paid according to the clock on earth, because the clock on the space ship runs slow when it approaches the speed of light.

Chapter 29 Relativity Q.6CQ
According to the theory of relativity, the maximum speed foi any particle is the speed of light. Is there a similar restriction on the maximum energy of a particle? Is there a maximum momentum? Explain.
Solution:
mastering-physics-solutions-chapter-29-relativity6cqs

Chapter 29 Relativity Q.6P
A neon sign in front of a café flashes on and off once every 4.1 s, as measured by the head cook. How much time elapses between flashes of the sign as measured by an astronaut in a spaceship moving toward Earth With a speed of 0.84c?
Solution:
mastering-physics-solutions-chapter-29-relativity6ps

Chapter 29 Relativity Q.7CQ
Give an argument that shows that аn object of finite mass cannot be accelerated from rest to a speed greater than the speed of light in a vacuum.
Solution:
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Chapter 29 Relativity Q.7P
A lighthouse sweeps its beam of light around in a circle once every 7.5 s. To an observer in a spaceship moving, away from Earth, the beam of light completes one full circle every 15 s. What is the speed of the spaceship relative to Earth?
Solution:
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Chapter 29 Relativity Q.8P
Refer to Example 29–1. How much does Benny age if he travels to Vega with a speed of 0.9995c?
Solution:
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Chapter 29 Relativity Q.9P
As a spaceship flies past with speed v, you observe that 1.0000 s elapses on the ship’s clock in the same time that 1.0000 min elapses on Earth. How fast is the ship traveling, relative to the Earth? (Express your answer as a fraction of the speed of light.)
Solution:
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Chapter 29 Relativity Q.10P
Donovan Bailey set a world record for the 100-m dash on July 27, 1996. If observers on a spaceship moving with a speed of 0.7705c relative to Earth saw Donovan Bailey’s run and measured his time to be 15.44 s, find the time that was recorded on Earth.
Solution:
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Chapter 29 Relativity Q.11P
Find the average distance (in the Earth’s frame of reference) covered by the muons in Example 29–2 if their speed relative to Earth is 0.750c.
Solution:
mastering-physics-solutions-chapter-29-relativity11ps

Chapter 29 Relativity Q.12P
The Pi Meson An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.6 × 10–8 s when at rest. If a pion moves with a speed of 0.99c relative to Earth, find (a) the average lifetime of the pion as measured by an observer on Earth and (b) the average distance traveled by the pion as measured by the same observer, (c) How far would the pion have traveled relative to Earth if relativistic time dilation did not occur?
Solution:
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Chapter 29 Relativity Q.13P
The Σ– Particle The Σ– is an exotic particle that has a lifetime (when at rest) of 0.15 ns. How fast would it have to travel in order for its lifetime, as measured by laboratory clocks, to be 0.25 ns?
Solution:
mastering-physics-solutions-chapter-29-relativity13ps

Chapter 29 Relativity Q.14P
IP (a) Is it possible for you to travel far enough and fast enough so that when you return from a trip, you are younger than your stay-at-home sister, who was born 5.0 y after you? (b) Suppose you fly on a rocket with a speed v = 0.99c for 1 y, according to the ship’s clocks and calendars. How much time elapses on Earth during your 1-y trip? (c) If you were 22 y old when you left home and your sister was 17, what are your ages when you return?
Solution:
mastering-physics-solutions-chapter-29-relativity14ps

Chapter 29 Relativity Q.15P
The radar antenna on a navy ship rotates with an angular speed of 0.29 rad/s. What is the angular speed of the antenna as measured by an observer moving away from the antenna with a speed of 0.82c?
Solution:
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Chapter 29 Relativity Q.16P
An observer moving toward Earth with a speed of 0.95c notices that it takes 5.0 min for a person to fill her car with gas. Suppose, instead, that the observer had been moving away from Earth with a speed of 0.80c. How much time would the observer have measured for the car to be filled in this case?
Solution:
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Chapter 29 Relativity Q.17P
IP An astronaut moving with a speed of 0.65c relative to Earth measures her heart rate to be 72 beats per minute, (a) When an Earth-based observer measures the astronaut’s heart rate, is the result greater than, less than, or equal to 72 beats per minute? Explain. (b) Calculate the astronaut’s heart rate as measured on Earth.
Solution:
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Chapter 29 Relativity Q.18P
BIO Newly sprouted sunflowers can grow at the rate of 0.30 in. per day. One such sunflower is left on Earth, and an identical one is placed on a spacecraft that is traveling away from Earth with a speed of 0.94c. How tall is the sunflower on the spacecraft when a person on Earth says his is 2.0 in. high?
Solution:
mastering-physics-solutions-chapter-29-relativity18ps

Chapter 29 Relativity Q.19P
An astronaut travels to Mars with a speed of 8350 m/s. After a month (30.0 d) of travel, as measured by clocks on Earth, how much difference is there between the Earth clock and the spaceship clock? Give your answer in seconds.
Solution:
mastering-physics-solutions-chapter-29-relativity19ps

Chapter 29 Relativity Q.20P
As measured in Earth’s frame of reference, two planets are 424,000 km apart. A spaceship flies from one planet to the other with a constant velocity, and the clocks on the ship show that the trip lasts only 1.00 s. How fast is the ship traveling?
Solution:
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Chapter 29 Relativity Q.21P
Captain Jean-Luc is piloting the USS Enterprise XXIII at a constant speed v = 0.825c. As the Enterprise passes the planet Vulcan, he notices that Ms watch and the Vulcan clocks both read 1:00 p.m. At 3:00 p.m., according to his watch, the Enterprise passes the planet Endor. If the Vulcan and Endor clocks are synchronized with each other, what time do the Endor clocks read when the Enterprise passes by?
Solution:
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Chapter 29 Relativity Q.22P
IP A plane flies with a constant velocity of 222 m/s. The clocks on the plane show that it takes exactly 2.00 h to travel a certain distance, (a) According to ground-based clocks, will the flight take slightly more or slightly less than 2.00 h? (b) Calculate how much longer or shorter than 2.00 h this flight will last, according to clocks on the ground.
Solution:
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Chapter 29 Relativity Q.23P
CE Tf the universal speed of light in a vacuum were larger than 3.00 X 108 m/s, would the effects of length contraction be greater or less than they are now? Explain.
Solution:
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Chapter 29 Relativity Q.24P
How fast does a 250-m spaceship move relative to an observer who measures the ship’s length to be 150 m?
Solution:
mastering-physics-solutions-chapter-29-relativity24ps

Chapter 29 Relativity Q.25P
Suppose the speed of light in a vacuum were only 25.0 mi/h. Find the length of a bicycle being ridden at a speed of 20.0 mi/h as measured by an observer sitting on a park bench, given that its proper length is 1.89 m.
Solution:
mastering-physics-solutions-chapter-29-relativity25ps

Chapter 29 Relativity Q.26P
A rectangular painting is 124 cm wide and 80.5 cm high, as indicated in Figure 29–29. At what speed, v, must the painting move parallel to its width if it is to appear to be square?
mastering-physics-solutions-chapter-29-relativity26p
Solution:
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Chapter 29 Relativity Q.27P
The Linac portion of the Fermilab Tevatron contains a high-vacuum tube that is 64 m long, through which protons travel with an average speed v = 0.65c. How long is the Linac tube, as measured in the proton’s frame of reference?
Solution:
mastering-physics-solutions-chapter-29-relativity27ps

Chapter 29 Relativity Q.28P
A cubical box is 0.75 m on a side, (a) What are the dimensions of the box as measured by an observer moving with a speed of 0.88c parallel to one of the edges of the box? (b) What is the volume of the box, as measured by this observer?
Solution:
mastering-physics-solutions-chapter-29-relativity28ps

Chapter 29 Relativity Q.29P
When parked, your car is 5.0 m long. Unfortunately, your garage is only 4.0 m long, (a) How fast would your car have to be moving for an observer on the ground to find your car shorter than your garage? (b) When you are driving at this speed, how long is your garage, as measured in tire car’s frame of reference?
Solution:
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Chapter 29 Relativity Q.30P
An astronaut travels to a distant star with a speed of 0.55c relative to Earth. From the astronaut’s point of view, the star is 7.5 ly from Earth. On the return trip, the astronaut travels with a speed of 0.89c relative to Earth. What is the distance covered on the return trip, as measured by the astronaut? Give your answer in light-years.
Solution:
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Chapter 29 Relativity Q.31P
IP Laboratory measurements show that an electron traveled 3.50 cm in a time of 0.200 ns. (a) In the rest frame of the electron, did the lab travel a distance greater than or less than 3.50 cm? Explain, (b) What is the electron’s speed? (c) In the electron’s frame of reference, how far did the laboratory travel?
Solution:
mastering-physics-solutions-chapter-29-relativity31ps

Chapter 29 Relativity Q.32P
You and a friend travel through space in identical spaceships. Your friend informs you that he has made some length measurements and that his ship is 150 m long but that yours is only 120 m long. From your point of view, (a) how long is your friend’s ship, (b) how long is your ship, and (c) what is the speed of your friend’s ship relative to yours?
Solution:
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Chapter 29 Relativity Q.33P
A ladder 5.0 m long leans against a wall inside a spaceship. From the point of view of a person on the ship, the base of the ladder is 3.0 m from the wall, and the top of the ladder is 4.0 m above the floor. The spaceship moves past the Earth with a speed of 0.90c in a direction parallel to the floor of the ship. Find the angle the ladder makes with the floor as seen by an observer on Earth.
Solution:
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Chapter 29 Relativity Q.34P
When traveling past an observer with a relative speed v, a rocket is measured to be 9.00 m long. When the rocket moves with a relative speed 2v, its length is measured to be 5.00 m. (a) What is the speed v? (b) What is the proper length of the rocket?
Solution:
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Chapter 29 Relativity Q.35P
IP The starships Picard and La Forge are traveling in the same direction toward the Andromeda galaxy. The Picard moves with a speed of 0.90c relative to the La Forge. A person on the La Forge measures the length of the two ships and finds the same value, (a) Tf a person on the Picard also measures the lengths of the two ships, which of the following is observed : (i) the Picard is longer; (ii) the La Forge is longer; or (iii) both ships have the same length? Explain, (b) Calculate the ratio of the proper length of the Picard to the proper length of the La Forge.
Solution:
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Chapter 29 Relativity Q.36P
A spaceship moving toward Earth with a speed of 0.90c launches a probe in the forward direction with a speed of 0.10c relative to the ship. Find the speed of the probe relative to Earth.
Solution:
mastering-physics-solutions-chapter-29-relativity36ps

Chapter 29 Relativity Q.37P
Suppose the probe in Problem 36 is launched in the opposite direction to the motion of the spaceship. Find the speed of the probe relative to Earth in this case.
Solution:
mastering-physics-solutions-chapter-29-relativity37ps

Chapter 29 Relativity Q.38P
A spaceship moving relative to an observer with a speed of 0.70c shines a beam of light in the forward direction, directly toward the observer. Use Equation 29–4 to calculate the speed of the beam of light relative to the observer.
Solution:
mastering-physics-solutions-chapter-29-relativity38ps

Chapter 29 Relativity Q.39P
Suppose the speed of light is 35 mi/h. A paper girl riding a bicycle at 22 mi/h throws a rolled-up newspaper in the forward direction, as shown in Figure 29–30. If the paper is thrown with a speed of 19 mi /h relative to the bike, what is its speed, v, with respect to the ground?
FIGURE 29–30
mastering-physics-solutions-chapter-29-relativity39p
Solution:
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Chapter 29 Relativity Q.40P
Two asteroids head straight for Earth from the same direction. Their speeds relative to Earth are 0.80c for asteroid 1 and 0.60c for asteroid 2. Find the speed of asteroid 1 relative to asteroid 2.
Solution:
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Chapter 29 Relativity Q.41P
Two rocket ships approach Earth from opposite directions, each with a speed of 0.8c relative to Earth. What is the speed of one ship relative to the other?
Solution:
mastering-physics-solutions-chapter-29-relativity41ps

Chapter 29 Relativity Q.42P
A spaceship and an asteroid are moving in the same direction away from Earth with speeds of 0.77c and 0.41c, respectively. What is the relative speed between the spaceship and the asteroid?
Solution:
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Chapter 29 Relativity Q.43P
An electron moves to the right in a laboratory accelerator with a speed of 0.84c. A second electron in a different accelerator moves to the left with a speed of 0.43c relative to the first electron. Find the speed of the second electron relative to the lab.
Solution:
mastering-physics-solutions-chapter-29-relativity43ps

Chapter 29 Relativity Q.44P
IP Two rocket ships are racing toward Earth, as shown in Figure 29–31. Ship A is in the lead, approaching the Earth at 0.80c and separating from ship В with a relative speed of 0.50c. (a) As seen from Earth, what is the speed, v, of Ship B? (b) If ship A increases its speed by 0.10c relative to the Earth, does the relative speed between ship A and ship В increase by 0.10c, by more than 0.10c, or by less than 0.10c? Explain, (c) Find the relative speed between ships A and В for the situation described in part (b).
mastering-physics-solutions-chapter-29-relativity44p
Solution:
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Chapter 29 Relativity Q.45P
IP An inventor has proposed a device that will accelerate objects to speeds greater than c. He proposes to place the object to be accelerated on a conveyor belt whose speed is 0.80c. Next, the entire system is to be placed on a second conveyor belt that also has a speed of 0.80c, thus producing a final speed of 1.6c.
(a) Construction details aside, should you invest in this scheme?
(b) What is the actual speed of the object relative to the ground?
Solution:
mastering-physics-solutions-chapter-29-relativity45ps

Chapter 29 Relativity Q.46P
A 4.5 × 106-kg spaceship moves away from Earth with a speed of 0.75c. What is the magnitude of the ship’s (a) classical and (b) relativistic momentum?
Solution:
mastering-physics-solutions-chapter-29-relativity46ps

Chapter 29 Relativity Q.47P
An asteroid with a mass of 8.2 × 1011 kg is observed to have a relativistic momentum of magnitude 7.74 × 1020 kg • m/s. What is the speed of the asteroid relative to the observer?
Solution:
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Chapter 29 Relativity Q.48P
An object has a relativistic momentum that is 7.5 times greater than its classical momentum. What is its speed?
Solution:
mastering-physics-solutions-chapter-29-relativity48ps

Chapter 29 Relativity Q.49P
A football player with a mass of 88 kg and a speed of 2.0 m/s collides head-on with a player from the opposing team whose mass is 120 kg. The players stick together and are at rest after the collision. Find the speed of the second player, assuming the speed of light is 3.0 m/s.
Solution:
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Chapter 29 Relativity Q.50P
In the previous problem, suppose the speed of the second player is 1.2 m/s. What is the speed of the players after the collision?
Solution:
mastering-physics-solutions-chapter-29-relativity50ps
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Chapter 29 Relativity Q.51P
A space probe with a rest mass of 8.2 × 107 kg and a speed of 0.50c smashes into an asteroid at rest and becomes embedded within it. If the speed of the probe-asteroid system is 0.26c after the collision, what is the rest mass of the asteroid?
Solution:
mastering-physics-solutions-chapter-29-relativity51ps
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Chapter 29 Relativity Q.52P
At what speed does the classical momentum, p = mv, give an error, when compared with the relativistic momentum, of (a) 1.00% and (b)’5.00%?
Solution:
mastering-physics-solutions-chapter-29-relativity52ps
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Chapter 29 Relativity Q.53P
A proton has 1836 times the rest mass of an electron. At what speed will an electron have the same momentum as a proton moving at 0.0100c?
Solution:
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Chapter 29 Relativity Q.54P
СE Particles A through D have the following rest energies and total energies:
mastering-physics-solutions-chapter-29-relativity54p
Rank these particles in order of increasing (a) rest mass, (b) kinetic energy, and (c) speed. Indicate ties where appropriate.
Solution:
mastering-physics-solutions-chapter-29-relativity54ps
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Chapter 29 Relativity Q.55P
Find the work that must be done on a proton to accelerate it from rest to a speed of 0.90c.
Solution:
mastering-physics-solutions-chapter-29-relativity55ps
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Chapter 29 Relativity Q.56P
If a neutron moves with a speed of 0.99c, what are its (a) total energy, (b) rest energy, and (c) kinetic energy?
Solution:
mastering-physics-solutions-chapter-29-relativity56ps
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Chapter 29 Relativity Q.57P
A spring with a force constant of 584 N/m is compressed a distance of 39 cm. Find the resulting increase in the spring’s mass.
Solution:
mastering-physics-solutions-chapter-29-relativity57ps

Chapter 29 Relativity Q.58P
When a certain capacitor is charged, its mass increases by 8.3 × 10−16 kg. How much energy is stored in the capacitor?
Solution:
mastering-physics-solutions-chapter-29-relativity58ps

Chapter 29 Relativity Q.59P
What minimum energy must a gamma ray have to create an electron-antielectron pair?
Solution:
mastering-physics-solutions-chapter-29-relativity59ps

Chapter 29 Relativity Q.60P
When a proton encounters an antiproton, the two particles annihilate each other, producing two gamma rays. Assuming the particles were at rest when they annihilated, find the energy of each of the two gamma rays produced. (Note: Tire rest energies of an antiproton and a proton are identical.)
Solution:
mastering-physics-solutions-chapter-29-relativity60ps

Chapter 29 Relativity Q.61P
A rocket with a mass of 2.7 × 106 kg has a relativistic kinetic energy of 2.7 × 1023 J. How fast is the rocket moving?
Solution:
mastering-physics-solutions-chapter-29-relativity61ps
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Chapter 29 Relativity Q.62P
A rocket with a mass of 2.7 × 106 kg has a relativistic kinetic energy of 2.7 × 1023 J. How fast is the rocket moving?
Solution:
mastering-physics-solutions-chapter-29-relativity62ps

Chapter 29 Relativity Q.63P
A nuclear power plant produces an average of 1.0 × 103 MW of power during a year of operation. Find the corresponding change in mass of reactor fuel, assuming all of the energy released by the fuel can be converted directly to electrical energy. (In a practical reactor, only a relatively small fraction of the energy can be converted to electricity.)
Solution:
mastering-physics-solutions-chapter-29-relativity63ps

Chapter 29 Relativity Q.64P
A helium atom has a rest mass of mHe = 4.002603 u. When disassembled into its constituent particles (2 protons, 2 neutrons, 2 electrons), the well-separated individual particles have the following masses: mp = 1.007276 u, mn = 1.008665 u, me = 0.000549 u. How much work is required to completely disassemble a helium atom? (Note: 1 u of mass has a rest energy of 931.49 MeV.)
Solution:
mastering-physics-solutions-chapter-29-relativity64ps
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Chapter 29 Relativity Q.65P
mastering-physics-solutions-chapter-29-relativity65p
Solution:
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Chapter 29 Relativity Q.66P
A proton has 1836 times the rest mass of an electron. At what speed will an electron have the same kinetic energy as a proton moving at 0.0250c?
Solution:
mastering-physics-solutions-chapter-29-relativity66ps
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Chapter 29 Relativity Q.67P
IP Consider a baseball with a rest mass of 0.145 kg. (a) How much work is required to increase the speed of the baseball from 25.0 m/s to 35.0 m/s? (b) Is the work required to increase the speed of the baseball from 200,000,025 m/s to 200,000,035 m/s greater than, less than, or the same as the amount found in part (a)? Explain, (c) Calculate the work required for the increase in speed indicated in part (b).
Solution:
mastering-physics-solutions-chapter-29-relativity67ps
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Chapter 29 Relativity Q.68P
IP A particle has a kinetic energy equal to its rest energy, (a) What is the speed of this particle? (b) If the kinetic energy of this particle is doubled, does its speed increase by a more than, less than, or exactly a factor of 2? Explain. (c) Calculate the speed of a particle whose kinetic energy is twice its rest energy.
Solution:
mastering-physics-solutions-chapter-29-relativity68ps
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Chapter 29 Relativity Q.69P
A lump of putty with a mass of 0.240 kg and a speed of 0.980c collides head-on and sticks to an identical lump of putty moving with the same speed. After the collision the system is at rest. What is the mass of the system after the collision?
Solution:
mastering-physics-solutions-chapter-29-relativity69ps
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Chapter 29 Relativity Q.70P
Find the radius to which the Sun must be compressed for it to become a black hole.
Solution:
mastering-physics-solutions-chapter-29-relativity70ps

Chapter 29 Relativity Q.71P
The Black Hole in the Center of the Milky Way Recent measurements show that the black hole at the center of the Milky Way galaxy, which is believed to coincide with the powerful radio source Sagittarius A*, is 2.6 million times more massive than the Sun; that is, M = 5.2 × 1036 kg. (a) What is the maximum radius of this black hole? (b) Find the acceleration of gravity at the Schwarzschild radius of this black hole, using the expression for R given in Equation 29–10. (c) How does your answer to part (b) change if the mass of the black hole is doubled? Explain.
Solution:
mastering-physics-solutions-chapter-29-relativity71ps
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Chapter 29 Relativity Q.72GP
CE Two observers are moving relative to one another. Which of the following quantities will they always measure to have the same value: (a) their relative speed; (b) the time between two events; (c) the length of an object; (d) the speed of light in a vacuum; (e) the speed of a third observer?
Solution:
Here two observers are moving relative to one another so they measure that they have the same speed relative to one another. Also according to the second postulate of special theory of relativity the speed of light is c in vacuum in all inertial frames of references. So the two observers will always measure
(a) The relative speed and
(d) The speed of light in vacuum have the same value, the remaining are the time between two events, length of an object and speed of a third observer are different for different observers.

Chapter 29 Relativity Q.73GP
CE You are standing next to a runway as an airplane kinds, (a) If you and the pilot observe a clock in the cockpit, which of you measures the proper time? (b) If you and the pilot observe a large clock on the control tower, which of you measures the proper time? (c) Which of you measures the proper length of the airplane? (d) Which of you measures the proper length of the runway?
Solution:
(a) The pilot will measure the correct proper time of the cockpit clock because the he is in rest frame of reference with respect to the clock. So pilot will observe correct proper time in the clock which is in cock pit.
(b) You measure the correct proper time in the large clock on the control tower, because you are in the rest frame of reference with respect to the clock on the control tower.
(c) The pilot measures the correct proper length of the aero plane. Because pilot is in the rest frame of reference with respect to the aero plane.
(d) You measure the correct proper length of the runway because you are in the rest frame with respect to the runway.

Chapter 29 Relativity Q.74GP
CE Which clock runs slower relative to a clock on the North Pole: clock on an airplane flying from New York to Los Angeles, or clock 2 on an airplane flying from Los Angeles to New York? Assume each plane has the same speed relative to the surface of the Earth. Explain.
Solution:
Clock 2 on an airplane flying from Los Angeles to New York runs slower than clock 1 on an airplane flying from New York to Los Angeles because its speed relative to the axis of the spinning earth is greater than the speed of other airplane.
Here the airplane which has the clock 2 has greater speed because the direction of motion of this airplane is in the same direction of the axis of the spinning earth.
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Chapter 29 Relativity Q.75GP
CE An apple drops from the bough of a tree to the ground. Is the mass of the apple near the top of its fall greater than, less than, or the same as its mass after it has landed? Explain.
Solution:
Let h be the height of apple in the bough of a tree from the ground.
If the apple is at the near top of its fall, i.e. at greater height h then t the earth- apple system has more gravitational potential energy. Hence this increased energy is equivalent to the increased mass according to the Einstein’s mass-energy equivalence relation. E = m\({ c }^{ 2 }\)
So the mass of the apple near the top of its fall is greater

Chapter 29 Relativity Q.76GP
CE Predict/Explain Consider two apple pies that are identical in every respect, except that pie 1 is piping hot and pie 2 is at room temperature, (a) If identical forces are applied to the two pies, is the acceleration of pie 1 greater than, less than, or equal to the acceleration of pie 2? (b) Choose the best explanation from among the following:

  • The acceleration of pie 1 is greater because the fact that it is hot means it has the greater energy.
  • The fact that pie 1 is hot means it behaves as if it has more mass than pie 2, and therefore it has a smaller acceleration.
  • The pies have the same acceleration regardless of their temperature because they have identical rest masses.

Solution:
a) Acceleration of pie 1 is less than pie 2
(b) Here pie1 is hotter than the pie2. That means the pie 1 has more energy than the pie 2. Therefore the pie1 is more massive than the pie 2.
So when we apply same force to the two pies, the massive pie will have less acceleration. Therefore acceleration of pie 1 is less than the acceleration of pie 2. Therefore option II is correct.

Chapter 29 Relativity Q.77GP
CE Is the mass of a warm cup of tea greater than, less than, or the same as the mass of the same cup of tea when it has cooled? Explain.
Solution:
The Einstein’s mass – energy equivalence relationship E = m\({ c }^{ 2 }\)
From this formula we can say that the energy (E) and mass (m) of a particle are directly proportional to each other. The warm cup of tea has more energy than the same cup of tea when it has cooled. So by using the above relation the mass of warm cup of tea is greater than the mass of the same cup of tea when it has cooled.

Chapter 29 Relativity Q.78GP
CE Predict/Explain An uncharged capacitor is charged by moving some electrons from one plate of the capacitor to the other plate, (a) Is the mass of the charged capacitor greater than, less than, or the same as the mass of the uncharged capacitor? (b) Choose the best explanation from among the following:

  • The charged capacitor has more mass because it is storing energy within it, just like a compressed spring.
  • The charged capacitor has less mass because some of its mass now appears as the energy of the electric field between its plates.
  • The capacitor has the same mass whether it is charged or not because charging it only involves moving electrons from one plate to the other without changing the total number of electrons.

Solution:
(a) Mass of charged capacitor is greater than the mass of uncharged capacitor.
(b) Option I is correct
The charged capacitor has more mass because it is storing energy within it, just like a compressed spring.

Chapter 29 Relativity Q.79GP
Cosmic Rays Protons in cosmic rays have been observed with kinetic energies as large as 1.0 × 1020 eV. (a) How fast are these protons moving? Give your answer as a fraction of the speed of light, (b) Show that the kinetic energy of a single one of these protons is much greater than the kinetic energy of a 15-mg ant walking with a speed of 8.8 mm/s.
Solution:
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Chapter 29 Relativity Q.80GP
An apple falls from a tree, landing on the ground 3.7 m below. How long is the apple in the air, as measured by an observer moving toward Earth with a speed of 0.89c?
Solution:
mastering-physics-solutions-chapter-29-relativity80ps
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Chapter 29 Relativity Q.81GP
What is the momentum of a proton with 1.50 × 103 MeV of kinetic energy? (Note: The rest energy of a proton is 938 MeV.)
Solution:
mastering-physics-solutions-chapter-29-relativity81ps
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Chapter 29 Relativity Q.82GP
IP A container holding 2.00 moles of an ideal monatomic gas is heated at constant volume until the temperature of the gas increases by 112 F°. (a) Does the mass of the gas increase, decrease, or stay the same? Explain, (b) Calculate the change in mass of the gas, if any.
Solution:
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Chapter 29 Relativity Q.83GP
Al4C nucleus, initially at rest, emits a beta particle. The beta particle is an electron with 156 keV of kinetic energy, (a) What is the speed of the beta particle? (b) What is the momentum of the beta particle? (c) What is the momentum of the nucleus after it emits the beta particle? (d) What is the speed of the nucleus after it emits the beta particle?
Solution:
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Chapter 29 Relativity Q.84GP
A clock at rest has a rectangular shape, with a width of 24 cm and a height of 12 cm. When this clock moves parallel to its width with a certain speed v its width and height are the same. Relative to a clock at rest, how long does it take for the moving clock to advance by 1.0 s?
Solution:
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Chapter 29 Relativity Q.85GP
A starship moving toward Earth with a speed of 0.75c launches a shuttle craft in the forward direction. Tire shuttle, which has a proper length of 12.5 m, is only 6.25 m long as viewed from Earth. What is the speed of the shuttle relative to the starship?
Solution:
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Chapter 29 Relativity Q.86GP
When a particle of charge q and momentum p enters a uniform magnetic field at right angles it follows a circular path of radius R = p/qB, as shown in Figure 29–32. What radius does this expression predict for a proton traveling with a speed v = 0.99c through a magnetic field В = 0.20 T if you use (a) the nonrelativistic momentum (p = mv) or (b) the relativistic momentum
Solution:
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Chapter 29 Relativity Q.87GP
IP A starship moving away from Earth with a speed of 0.75c launches a shuttle craft in the reverse direction, that is, toward Earth. (a) If the speed of the shuttle relative to the starship is 0.40c, and its proper length is 13 m, how long is the shuttle as measured by an observer on Earth? (b) If the shuttle had been launched in the forward direction instead, would its length as measured by an observer on Earth be greater than, less than, or the same as the length found in part (a)? Explain. (c) Calculate the length for the case described in part (b).
Solution:
mastering-physics-solutions-chapter-29-relativity87ps
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Chapter 29 Relativity Q.88GP
A 2.5-m titanium rod in a moving spacecraft is at an angle of 45° with respect to the direction of motion. The craft moves directly toward Earth at 0.98c. As viewed from Earth, (a) how long is the rod and (b) what angle does the rod make with the direction of motion?
Solution:
mastering-physics-solutions-chapter-29-relativity88ps
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Chapter 29 Relativity Q.89GP
Electrons are accelerated from rest through a potential difference of 276,000 V. What is the final speed predicted (a) classically and (b) relativistically?
Solution:
mastering-physics-solutions-chapter-29-relativity89ps
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Chapter 29 Relativity Q.90GP
IP In Conceptual Checkpoint 29-2 we considered an astronaut at rest on an inclined bed inside a moving spaceship. From the point of view of observer 1, on board the ship, the astronaut has a length L0 and is inclined at an angle θ0 above the floor. Observer 2 sees the spaceship moving to the right with a speed v.
mastering-physics-solutions-chapter-29-relativity90p
Suppose a pion (a subatomic particle) is observed to have a kinetic energy K = 35.0 MeV and a momentum p = 5.61 × 1020 kg3 m/s = 105 MeV/c. What is the rest energy of the pion? Give your answer in MeV.
Solution:
mastering-physics-solutions-chapter-29-relativity90ps

Chapter 29 Relativity Q.91GP
A small star of mass m orbits a supermassive black hole of mass M. (a) Find the orbital speed of the star if its orbital radius is 2R, where R is the Schwarzschild radius (Equation 29–10). (b) Repeat part (a) for an orbital radius equal to R.
Solution:
mastering-physics-solutions-chapter-29-relativity91ps
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Chapter 29 Relativity Q.92GP
IP Consider a “relativistic air track” on which two identical air carts undergo a completely inelastic collision. One cart is initially at rest; the other has an initial speed of 0.650c. (a) In classical physics, the speed of the carts after the collision would be 0.325c. Do you expect the final speed in this relativistic collision to be greater than or less than 0.325c? Explain, (b) Use relativistic momentum conservation to find the speed of the carts after they collide and stick together.
Solution:
mastering-physics-solutions-chapter-29-relativity92ps
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Chapter 29 Relativity Q.93GP
IP In Conceptual Checkpoint 29-2 we considered an astronaut at rest on an inclined bed inside a moving spaceship. From the point of view of observer 1, on board the ship, the astronaut has a length L0 and is inclined at an angle θ0 above the floor. Observer 2 sees the spaceship moving to the right with a speed v.
mastering-physics-solutions-chapter-29-relativity93p
Solution:
mastering-physics-solutions-chapter-29-relativity93ps
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Chapter 29 Relativity Q.94GP
A pulsar is a collapsed, rotating star that sends out a narrow beam of radiation, like the light from a lighthouse. With each revolution, we see a brief, intense pulse of radiation from the pulsar. Suppose a pulsar is receding directly away from Earth with a speed of 0.800c, and the starship Endeavor is sent out toward the pulsar with a speed of 0.950c relative to Earth. If an observer or Earth finds that 153 pulses are emitted by the pulsar every second, at what rate does an observer on the Endeavor see pulses emitted?
Solution:
mastering-physics-solutions-chapter-29-relativity94ps
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Chapter 29 Relativity Q.95GP
Show that the total energy of an object is related to its momentum by the relation E2 = p2c2 + (m0c2)2.
Solution:
mastering-physics-solutions-chapter-29-relativity95ps

Chapter 29 Relativity Q.96GP
Show that if 0<v1<с and 02<с are two velocities pointing in the same direction, the relativistic sum of these velocities, v, is greater than v1 and greater than v2 but less than c. In particular, show that this is true even if v1 and v2 are greater than 0.5c.
Solution:
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Chapter 29 Relativity Q.97GP
Show that an object with momentum p and rest mass m0 has a speed given by
mastering-physics-solutions-chapter-29-relativity97p
Solution:
mastering-physics-solutions-chapter-29-relativity97ps
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Chapter 29 Relativity Q.98GP
Decay of the ∑− Particle When at rest, the ∑− particle has a lifetime of 0.15 ns before it decays into a neutron and a pion. One particular particle is observed to travel 3.0 cm in the lab before decaying. What was its speed?
Solution:
mastering-physics-solutions-chapter-29-relativity98ps
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Chapter 29 Relativity Q.99PP
Find the speed of an electron accelerated through a voltage of 25.0 kV—ignoring relativity. Express your answer as a fraction times the speed of light. (Speeds over about 0.1c are generally regarded as relativistic.)
A. 0.221c
B. 0.281c
C. 0.312c
D. 0.781c
Solution:
mastering-physics-solutions-chapter-29-relativity99ps

Chapter 29 Relativity Q.100PP
When relativistic effects are included, do you expect the speed of the electrons to be greater than, less than, or the same as the result found in the previous problem?
Solution:
When the relativistic effects are induced then the speed of the electrons will be less than the speed we found in problem 99.

Chapter 29 Relativity Q.101PP
Find the speed of the electrons in Problem 99, this time using a correct relativistic calculation. As before, express your answer as a fraction times the speed of light.
A. 0.301c
B. 0.312c
C. 0.412c
D. 0.953c
Solution:
mastering-physics-solutions-chapter-29-relativity101ps
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Chapter 29 Relativity Q.102PP
Suppose the accelerating voltage in Problem 99 is increased by a factor of 10. What is the correct relativistic speed of an electron in this case?
A. 0.205c
B. 0.672c
C. 0.740c
D. 0.862c
Solution:
mastering-physics-solutions-chapter-29-relativity102ps
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Chapter 29 Relativity Q.103IP
Referring to Example 29?4 The Picard approaches star- base Faraway Point with a speed of 0.806c, and the La Forge approaches the starbase with a speed of 0.906c. Suppose the Picard now launches a probe toward tire starbase. (a) What velocity must the probe have relative to the Picard if it is to be at rest relative to the la Forge? (b) Win at velocity must the probe have relative to the Picard if its velocity relative to the La Forge is to be 0.100c? (c) For the situation described in part (b), what is the velocity of the probe relative to the Faraway Point starbase?
Solution:
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Chapter 29 Relativity Q.104IP
Referring to Example 29-4 Faraway Point starbase launches a probe toward the approaching starships. The probe has a velocity relative to the Picard of −0.906c. The Picard approaches starbase Faraway Point with a speed of 0.806c, and the La Forge approaches the starbase with a speed of 0.906c. (a) What is the velocity of the probe relative to the La Forge? (b) What is the velocity of the probe relative to Faraway Point starbase?
Solution:
mastering-physics-solutions-chapter-29-relativity104ps
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Mastering Physics Solutions Chapter 28 Physical Optics: Interference and Diffraction

Mastering Physics Solutions Chapter 28 Physical Optics: Interference and Diffraction

Mastering Physics Solutions

Chapter 28 Physical Optics: Interference and Diffraction Q.1CQ
When two light waves interfere destructively, what happens to their energy?
Solution:
When two waves interfere destructively at one place, then at some other place, these waves interfere constructively. The energy at the point of destructive interference at one place is always balanced by that at constructive interference. In destructive interference, the net energy of the resultant wave is less than the sum of energies of two individual waves, which interfere destructively to give destructive interference.
In constructive interference, the net energy of the resultant wave is more than the sum of energies of two individual waves which interfere constructively to give constructive interference. Thus, when two waves interfere destructively at one place, then the energy of individual waves at that place goes to the point where these waves constructively interfere. Thus, at a place of destructive interference, the energy is nearly zero, and at a place of constructive interference, energy is more than the sum of energies of individual waves. Hence, energy is redistributed from a place of destructive interference to a place of constructive interference.

Chapter 28 Physical Optics: Interference and Diffraction Q.1P
Two sources emit waves that are coherent, in phase, and have wavelengths of 26.0 m. Do the waves interfere constructively or destructively at an observation point 78.0 m from one source and 143 m from the other source?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction1ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction1ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.2CQ
What happens to the two-slit interference pattern if the separation between the slits is less than the wavelength of light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction2cqs

Chapter 28 Physical Optics: Interference and Diffraction Q.2P
Repeat Problem 1 for observation points that are
(a) 91.0 m and 221 m and
(b) 44.0 m and 135 m from the two sources.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction2ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction2ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.3CQ
If a radio station broadcasts its signal through two different antennas simultaneously, does this guarantee that the signal you receive will be stronger than from a single antenna? Explain.
Solution:
When a radio station broadcasts its signal through two different antennas may interfere destructively or constructively. Then the net intensity will be minimum or maximum. So the signals receiving from single antenna may be stronger than the signals receiving from the two antennas.

Chapter 28 Physical Optics: Interference and Diffraction Q.3P
Two sources emit waves that are in phase with each other. What is the longest wavelength that will give constructive interference at an observation point 161 m from one source and 295 m from the other source?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction3ps

Chapter 28 Physical Optics: Interference and Diffraction Q.4CQ
How would you expect the interference pattern of a two-slit experiment to change if white light is used instead of monochromatic light?
Solution:
In a two-slit interference pattern when a white light is used instead of monochromatic light then always the location of bright and dark fringes depends on the wavelength of light.
So each bright fringe formed on the screen splits up into seven different colors called ‘VIGB YOR’ (or) it also known as “rainbow” effect.

Chapter 28 Physical Optics: Interference and Diffraction Q.4P
A person driving at 17 m/s crosses the line connectingtwo radio transmitters at right angles, as shown in Figure 28–31. The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction4p
point A, the radio picks up a maximum net signal.
(a) What is the longest possible wavelength of the radio waves?
(b) How long after the car passes point A does the radio experience a minimum in the net signal? Assume that the wavelength has the value found in part (a).
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction4ps
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Chapter 28 Physical Optics: Interference and Diffraction Q.5CQ
Suppose a sheet of glass is placed in front of one of the slits in a two-slit experiment. If the thickness of the glass is such that the light reaching the two slits is 180° out of phase, how does this affect the interference pattern?
Solution:
If a sheet of glass is placed in front of one of the slits and the thickness of the glass is such that the light reaching the two slits is 180° out of phase. Then here in this case the interference pattern will be reversed.
Changing the phase of the light from one slit by 180°, results in destructive interference (a dark fringe) at the center of the pattern. Thus the entire fringe pattern will be reversed.

Chapter 28 Physical Optics: Interference and Diffraction Q.5P
Two students in a dorm room listen to a pure tone produced by two loudspeakers that are in phase. Students A and B in Figure 28–32 hear a maximum sound. What is the lowest possible frequency of the loudspeakers?
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Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction5ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction5ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.6CQ
Describe the changes that would be observed in the two-slit interference pattern if the entire experiment were to be submerged in water.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction6cqs

Chapter 28 Physical Optics: Interference and Diffraction Q.6P
If the loudspeakers in Problem 5 are 180° out of phase, determine whether a 185-Hz tone heard at location B is a maximum or a minimum.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction6p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction6ps

Chapter 28 Physical Optics: Interference and Diffraction Q.7CQ
Explain why the central spot in Newton’s rings is dark.
Solution:
When light incident from rarer to denser medium then there exist a phase difference of . When the light refracted from denser medium to rarer medium there will be no phase
change.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction7cqs

Chapter 28 Physical Optics: Interference and Diffraction Q.7P
A microphone is located on the line connecting two speakers that are 0.845 m apart and oscillating in phase. The microphone is 2.55 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphone’s location?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction7ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction7ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.8CQ
Two identical sheets of glass are coated with films of different materials but equal thickness. The colors seen in reflected light from the two films are different. Give a reason that can account for this observation.
Solution:
The color (wavelength) that reflects strongly depends on the index of refraction of the material of the film. As the two films have different index of refractive, so the interference in the thin films happens at different wavelengths. The phase change in reflection from the film – glass interface will be different for the two films. This results in different colors appearing in the reflected light.

Chapter 28 Physical Optics: Interference and Diffraction Q.8P
A microphone is located on the line connecting two speakers that are 0.845 m apart and oscillating 180° out of phase. The microphone is 2.25 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphone’s location?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction8ps
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Chapter 28 Physical Optics: Interference and Diffraction Q.9CQ
Spy cameras use lenses with very large apertures. Why are large apertures advantageous in such applications?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction9cqs

Chapter 28 Physical Optics: Interference and Diffraction Q.9P
Moe, Larry, and Curly stand in a line with a spacing of 1.00 m. Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in Figure 28–33. The speakers produce a single-frequency tone, vibrating in phase with each other. What are the two lowest frequencies that allow Larry to hear a loud tone while Moe and Curly hear very little?
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction9p
Solution:
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Chapter 28 Physical Optics: Interference and Diffraction Q.10CQ
A cat’s eye has a pupil that is elongated in the vertical direction. How does the resolution of a cat’s eye differ in the horizontal and vertical directions?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction10cqs

Chapter 28 Physical Optics: Interference and Diffraction Q.10P
IP In Figure 28–33 the two speakers emit sound that is 180° out of phase and of a single frequency, f.
(a) Does Larry hear a
sound intensity that is a maximum or a minimum? Does your answer depend on the frequency of the sound? Explain.
(b) Find the lowest two frequencies that produce amaximum sound intensity at the positions of Moe and Curly.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction10p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction10ps
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Chapter 28 Physical Optics: Interference and Diffraction
Which portion of the soap film in the accompanying photograph is thinnest? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction11cq
Solution:
The top of the film in the photograph appears black, so the soap film is thinnest at the top.
Light reflected from the front surface of the film has undergone a phase change of because the light is reflected at the surface backed by denser medium. The light that reflects from the back surface of the film does not undergo any phase change because the light is reflected at the surface backed by rarer medium. Therefore light from front & back surfaces of the film will undergo destructive interference as the path length between the surfaces goes to zero. This is why the top of the film where the film is thinnest, appears black in the photo.

Chapter 28 Physical Optics: Interference and Diffraction Q.11P
IP Suppose the car radio in Problem 4 picks up a minimum net signal at point A.
(a) What is the largest possible value for the wavelength of the radio waves? (b) If the radio transmitters use a wavelength that is half the value found in part (a), will the car radio pick up a net signal at point A that is a maximum or a minimum? Explain.
(c) What is the second largest wavelength that will result in a minimum signal at point A?
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction11p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction11ps

Chapter 28 Physical Optics: Interference and Diffraction Q.12CQ
The color of an iridescent object, like a butterfly wing or a feather, appears to be different when viewed from different directions. The color of a painted surface appears the saine from all viewing angles. Explain the difference.
Solution:
In iridescent objects. the colors are reflected through the process of thin film of interferenca There will be two reflections one from the top and one from the bottom of the thin film that then
constructively interfere The conditions for interference depends on path length and path length depends on the angle from which one views the film
A pointed object however reflects light of a given color. There is only one reflection at the surface of the points. So no matter what angle you view it from, it always reflects the same color It is the interference process for the thin film that causes the iridescence.

Chapter 28 Physical Optics: Interference and Diffraction Q.12P
CE Consider a two-slit interference pattern, with monochromatic light of wavelength λ. What is the path difference ∆ℓ for
(a) the fourth bright fringe and
(b) the third dark fringe above the centra] bright fringe? Give your answers in terms of the wavelength of the light.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction12ps

Chapter 28 Physical Optics: Interference and Diffraction Q.13P
CE
(a) Does the path-length difference ∆ℓ increase or decrease as you move from one bright fringe of a two-slit experiment to the next bright fringe farther out?
(b) What is ∆ℓ in terms of the wavelength λ of the light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction13ps

Chapter 28 Physical Optics: Interference and Diffraction Q.14P
CEPredict/Explain A two-slit experiment with red light produces a set of bright fringes.
(a) Will the spacing between the fringes increase, decrease, or stay the same if the color of the light is changed to blue?
(b) Choose the best explanation from among the following:
I. The spacing between the fringes will increase because blue light has a greater frequency than red light.
II. The fringe spacing decreases because blue light has a shorter wavelength than red light.
III. Only the wave property of light is important in producing the fringes, not the color of the light. Therefore the spacing stays the same.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction14ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction14ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.15P
CE Atwo-slit experiment with blue light produces a set of bright fringes. Will the spacing between the fringes increase, decrease, or stay the same if
(a) the separation of the slits is decreased, or
(b) the experiment is immersed in water?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction15ps

Chapter 28 Physical Optics: Interference and Diffraction Q.16P
Laser light with a wavelength λ = 670 nm illuminates a pair of slits at normal incidence. What slit separation will produce first-order maxima at angles of ±35° from the incident direction?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction16ps

Chapter 28 Physical Optics: Interference and Diffraction Q.17P
Monochromatic light passes through two slits separated by a distance of 0.0334 mm. If the angle to the third maximum above the central fringe is 3.21°, what is the wavelength of the light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction17ps

Chapter 28 Physical Optics: Interference and Diffraction Q.18P
In Young’s two-slit experiment, the first dark fringe above the central bright fringe occurs at an angle of 0.31°. What is the ratio of the siit separation, d, to the wavelength of the light,λ?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction18ps

Chapter 28 Physical Optics: Interference and Diffraction Q.19P
IP A two-slit experiment with slits separated by 48.0 × 10−5 m produces a second-order maximum at an angle of 0.0990°.
(a) Find the wavelength of the light used in this experiment.
(b) If the slit separation is increased but the second-order maximum stays at the same angle, does the wavelength increase, decrease, or stay the same? Explain.
(c) Calculate the wavelength for a slit separation of 68.0 × 10−5 m.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction19ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction19ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.20P
A two-slit pattern is viewed on a screen 1.00 m from the slits. If the two third-order minima are 22.0 cm apart, what is the width (in cm) of the centralbright fringe?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction20ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction20ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.21P
Light from a He-Ne laser (λ = 632.8 nm) strikes apair of slits at normal incidence, forming a double-slit interference pattern on a screen located 1.40 m from the slits. Figure 28–34
shows the interference pattern observed on the screen. What is the slit separation?
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction21p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction21ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction21ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.22P
Light with a wavelength of 546 nm passes through two slits and forms an interference pattern on a screen 8.75 m away. If the linear distance on the screen from the central fringe to the first bright fringe above it is 5.36 cm, what is the separadon of the slits?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction22ps
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Chapter 28 Physical Optics: Interference and Diffraction Q.23P
A set of parallel slits for optical interference can be made by holding two razor blades together (carefully!) and scratching a pair of lines on a glass microscope slide that has been painted black. When monochromatic light strikes these slits at normal incidence, an interference pattern is formed on a distant screen. The thickness of each razor blade used to make the slits is 0.230 mm, and the screen is 2.50 m from the slits, if the center-to-center separation of the fringes is 7.15 mm, what is the wavelength of the light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction23ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction23ps1
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Chapter 28 Physical Optics: Interference and Diffraction Q.24P
IP Suppose the interference pattern shown in Figure 28–34 is produced by monochromatic light passing through two slits, with a separation of 135 μm, and onto a screen 1.20 m away.
(a) What is the wavelength of the light?
(b) If the frequency of this light is increased, will the bright spots of the pattern move closer together or farther apart? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction24p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction24ps

Chapter 28 Physical Optics: Interference and Diffraction Q.25P
A physics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least 2.50 cm. If the slits have a separation d = 0.0220 mm, what is the minimum distance from the slits to the screen when 632.8-nm light from a He-Ne laser is used?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction25ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction25ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.26P
IP When green light (λ = 505 nm) passes through a pair of double slits, the interference pattern shown in Figure 28–35
(a) is observed. When light of a different color passes throughthe same pair of slits, the pattern shown in Figure 28–35
(b) is observed.
(a) Is the wavelength of the second color Longer or shorter than 505 nm? Explain.
(b) Find the wavelength of the second color. (Assume that the angles involved are small enough to set sin θ ≈ tan θ.)
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction26p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction26ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction26ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.27P
IP The interference pattern shown in Figure 28–35 (a) is produced by green light with a wavelength of λ = 505 nm passing through two slits with a separation of 127 μ m. After passing through the slits, the light forms a pattern of bright and dark spots on a screen located 1.25 m from the slits.
(a) What is the distance between the two vertical, dashed lilies in Figure 28–35 (a)?
(b) If it is desired to produce a more rightly packed interference pattern, like the one shown in Figure 28–35 (b), should the frequency of the light be increased or decreased? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction27p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction27ps
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Chapter 28 Physical Optics: Interference and Diffraction Q.28P
CE Figure 28–36 shows four different cases where light of wavelength λ reflects from both the top and the bottom of a thin film of thickness d. The indices of refraction of the film and the media above and below it are indicated in the figure. For which of the cases will the two reflected rays undergo constructive interference if
(a) d = λ/4 or
(b) d = λ/2?
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction28p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction28ps
Here, as shown in figure, it is clear that,
In figure (1), light travels from high refractive index to low refractive index in both situations. In this case, both waves are inverted, so they end up having no shift with respect to one another.
In figure (2), light travels from low refractive index to high refractive index in both cases. In this case, there is phase shift. In this case, neither of the waves is inverted, so they have also no shift with respect to one another.
In figure (3), light travels from low refractive index to high refractive index and then from high refractive index to low refractive index. In this case, when the light is refracted from low refractive wavelength to high refractive wavelength, then the waves is inverted, which is equivalent to half the wavelength shift and secondly when the light is refracted from the high refractive wavelength to low refractive wavelength, then it experiences no shift. This gives the effect that the waves are shifted by half a wavelength.
In figure (4), light travels from low refractive index to high refractive index and then from high refractive index to low refractive index. In this case, when the light is refracted from low refractive wavelength to high refractive wavelength, then the waves is inverted, which is equivalent to half the wavelength shift and secondly when the light is refracted from the high refractive wavelength to low refractive wavelength, then it experiences no shift. This gives the effect that the waves are shifted by half a wavelength.
This concludes:
For the figure (1) there is no phase shift.
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Chapter 28 Physical Optics: Interference and Diffraction Q.29P
CE The oil film floadng on water in the accompanying photo appears dark near the edges, where it is thinnest. Is the index of refraction of the oil greater than or less than that of the water? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction29p
Solution:
The light reflected from the top surface of the oil has its phase changed by half wavelength, since the refractive index of oil is greater than the refractive index of air. At the boundary between oil and water the reflected wave experiences no phase change if the refractive index of oil is greater than that of water. This must be the case, because where the oil is thinnest the phase difference between the light reflected from the top and bottom of the oil is just the phase difference due to the reflection – the phase difference due to the path length difference goes to zero. With a half wavelength phase change between light reflected from the top and bottom of the oil, light will undergo destructive interference and the film will appear dark. Therefore, a dark appearance near the edges implies oil has the greater refractive index than water.

Chapter 28 Physical Optics: Interference and Diffraction Q.30P
A soap bubble with walls 401 nm thick floats in air. If this bubble is illuminated perpendicularly with sunlight, what wavelength (and color) will be absent in the reflected light? Assume that the index of refraction of the soap film is 1.33. (Refer to Example 25-3 for the connection between wavelength and color.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction30ps

Chapter 28 Physical Optics: Interference and Diffraction Q.31P
A soap film (n = 1.33) is 825 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
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Chapter 28 Physical Optics: Interference and Diffraction Q.32P
White light is incident on a soap film (n = 1.30) in air. The reflected light looks bluish because the red light (λ = 670 nm) is absent in the reflection. What is the minimum thickness of the soap film?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction32ps

Chapter 28 Physical Optics: Interference and Diffraction Q.33P
A 742-nm-thick soap film (nfilm = 1.33) rests on a glass plate (nglass = 1.52). White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected from the film? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
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Chapter 28 Physical Optics: Interference and Diffraction Q.34P
An oil film (n = 1.38) floats on awater puddle. You notice that green light (λ = 521 nm) is absent in the reflection. What is the minimum thickness of the oil film?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction34ps

Chapter 28 Physical Optics: Interference and Diffraction Q.35P
A radio broadcast antenna is 36.00 km from your house. Suppose an airplane is flying 2.230 km above the line connecting the broadcast antenna and your radio, and that waves reflected from the airplane travel 88.00 wavelengths farther than waves that travel directly from the antenna to your house.
(a) Do you observe constructive or destructive interference
between the direct and reflected waves? (Hint: Does a phase change occur when the waves are reflected?)
(b) The situation just described occurs when the plane is above a point on the ground that is two-thirds of the way from the antenna to your house. What is the wavelength of the radio waves?
Solution:
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Chapter 28 Physical Optics: Interference and Diffraction Q.36P
IP Newton’s Rings Monochromatic light with λ = 648 nm shines down on a plano-convex lens lying on a piece of plate glass, as shown in Figure 28–37. When viewed from above, one sees a set of concentric dark and bright fringes, referred to as Newton’s rings (See Figure 28–11 for a photo of Newton’s rings.).
(a) If the radius of the twelfth dark ring from the center is measured to be 1.56 cm, what is the radius of curvature, R, of the lens?
(b) If light with a longer wavelength is used with this system, will the radius of the twelfth dark ring be greater than or less than 1.56 cm? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction36p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction36ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction36ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction36ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction36ps3

Chapter 28 Physical Optics: Interference and Diffraction Q.37P
Light is incident from above on two plates of glass, separated on both ends by small wires of diameter
d = 0.600 μ m. Considering only interference between light reflected from the bottom surface of the upper plate and light reflected from the upper surface of the lower plate, state whether the following wavelengths give constructive or destructive interference:
(a) λ = 600.0 nm;
(b) λ = 800.0 nm;
(c) λ = 343.0 nm.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction37ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction37ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction37ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.38P
(a) What is the minimum soap-film thickness (n = 1.33) in air that will produce constructive interference in reflection for red (λ = 652 nm) tight?
(b) Which visible wavelengths will destructively interfere when reflected from this film? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction38ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction38ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.39P
IP A thin layer of magnesium fluoride (n = 1.38) is used to coat a flint-glass lens (n = 1.61).
(a) What thickness should the magnesium fluoride film have if the reflection of 565-nm light is to be suppressed? Assume that the light is incident at right angles to the film.
(b) If it is desired to suppress the reflection of light with a higher frequency, should the coating of magnesium fluoride be made thinner or thicker? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction39ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction39ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction39ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.40P
White light is incident normally on a thin soap film (n = 1.33) suspended in air.
(a) What are the two minimum thicknesses that will constructively reflect yellow (λ = 590 nm) light?
(b) What arc the two minimum thicknesses that will destructively reflect yellow (λ = 590 nm) light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction40ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction40ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.41P
A thin coating (t = 340.0 nm, n = 1.480) is placed on a glass lens. Which visible (400 nm < λ < 700 nm) wavelength(s) will be absent in the reflected beam if
(a) the glass has an index of refraction n = 1.350, and
(b) the glass has an index of refraction n = 1.675?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction41ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction41ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction41ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction41ps3
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction41ps4

Chapter 28 Physical Optics: Interference and Diffraction Q.42P
Two glass plates are separated by fine wires with diameters d1 = 0.0500 mm and d2 = 0.0520 mm, as indicated in Figure 28–38. The wires are parallel and separated by a distance of 7.00 cm. If monochromatic light with λ = 589 nm is incident
from above, what is the distance (in cm) between adjacent dark bands in the reflected light? (Consider interference only between light reflected from the bottom surface of the upper plate and light reflected from the upper surface of the lower plate.)
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction42p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction42ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction42ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.43P
CE A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if
(a) the wavelength is doubled,
(b) the slit width is doubled, or
(c) the distance from the slit to the screen is doubled?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction43ps

Chapter 28 Physical Optics: Interference and Diffraction Q.44P
What width single slit will produce first-order diffraction minima at angles of ±23° from the central maximum with 690-nm light?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction44ps

Chapter 28 Physical Optics: Interference and Diffraction Q.45P
Diffraction also occurs with sound waves. Consider 1300-Hz sound waves diffracted by a door that is 84 cm wide. What is the angle between the two first-order diffraction minima?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction45ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction45ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.46P
Green light (λ = 546 nm) strikes a single slit atnormal incidence. What width slit will produce a central maximum that is 2.50 cm wide on a screen 1.60 m from the slit?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction46ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction46ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction46ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.47P
Light with a wavelength of 676 nm passes through a slit 7.64 μ mwide and falls on a screen 1.85 m away. Find the linear distance on the screen from the central bright fringe to the first bright fringe above it.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction47ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction47ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction47ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.48P
Repeat Problem 47, only this time find the distance on the screen from the central bright fringe to the third dark fringe above it.
IP A single slit is illuminated with 610-nm light, and the resulting diffraction pattern is viewed on a screen 2.3 m away.
(a) If the lineardistance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?
(b) If the slit is made wider, will the distance between the first and second dark fringes increase or decrease? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction48ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction48ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction48ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction48ps3

Chapter 28 Physical Optics: Interference and Diffraction Q.49P
IP A single slit is illuminated with 610-nm light, and the resulting diffraction pattern is viewed on a screen 2.3 m away.
(a) If the lineardistance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?
(b) If the slit is made wider, will the distance between the first and second dark fringes increase or decrease? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction49ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction49ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction49ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction49ps3

Chapter 28 Physical Optics: Interference and Diffraction Q.50P
How many dark fringes will be produced on either side of the central maximum if green light (λ = 553 nm) is incident on a slit that is 8.00 μ m wide?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction50ps

Chapter 28 Physical Optics: Interference and Diffraction Q.51P
IP The diffraction pattern shown in Figure 28–39 is produced by passing He-Ne laser light (λ = 632.8 nm) through a single slit and viewing the pattern an a screen 1.50 m behind the slit.
(a) What is the width of the slit?
(b) If monochromatic yellow light with a wavelength oi 591 nm is used with this slit instead, will the distance indicated in Figure 28–39 be greater than or less than 15.2 cm? Explain.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction51p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction51ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction51ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction51ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction51ps3

Chapter 28 Physical Optics: Interference and Diffraction Q.52P
A screen is placed 1.00 m behind a single slit. The central maximum in the resulting diffraction pattern on the screen is 1.60 cm wide—that is, the two first-order diffraction minima
are separated by 1.60 cm. What is the distance between the two second-order minima?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction52ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction52ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction52ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.53P
CE Predict/Explain
(a) In principle, do your eyes have greater resolution on a dark cloudy day or on a bright sunny day?
(b) Choose the best explanation from among the following:
I. Your eyes have greater resolution on a cloudy day because your pupils are open wider to allow more light to enter the eye.
II. Your eyes have greater resolution on a sunny day because the bright light causes your pupil to narrow down to a smaller opening.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction53ps

Chapter 28 Physical Optics: Interference and Diffraction Q.54P
CE Is resolution greater with blue light or red light, all other factors being equal? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction54ps

Chapter 28 Physical Optics: Interference and Diffraction Q.55P
Two point sources of light are separated by 5.5 cm. As viewed through a 12-μm-diameter pinhole, what is the maximum distance from which they can be resolved
(a) if red light (λ = 690 nm) is used, or
(b) if violet light (λ = 420 nm) is used?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction55ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction55ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction55ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.56P
A spy camera is said to be able to read the numbers on a car’s license plate. Tf the numbers on the plate are 5.0 cm apart, and the spy satellite is at an altitude of 160 km, what must be the diameter of the camera’s aperture? (Assume light with a wavelength of 550 nm.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction56ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction56ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.57P
Splitting Binary Stars As seen from Earth, the red dwarfs Krüger 60A and Krüger 60B form a binary star system with an angular separation of 2.5 arc seconds. What is the smallest diameter telescope that could theoretically resolve these stars using550-nm light? (Note: 1 arc sec = 1/3600°)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction57ps

Chapter 28 Physical Optics: Interference and Diffraction Q.58P
Find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person (2.0 m) from an SR-71 Blackbird airplane flying at an altitude of 27 km. (As-sume light with a wavelength of 450 nm.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction58ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction58ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.59P
The Resolution of Hubble The Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.4 m in diameter. If the HST were to look down on Earth’s surface (rather than up at the stars), what is the minimum separation of two objects that could be resolved using 550-nm light? [Note: The HST is used only for astronomical work, but a (classified) number of similar telescopes are in orbit for spy purposes.]
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction59ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction59ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction59ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.60P
A lens that is “optically perfect” is still limited by diffraction effects. Suppose a lens has a diameter of 120 mm and a focal length of 640 mm.
(a) Find the angular width (that is, the angle from the bottom to the top) of the central maximum in the diffraction pattern formed by this lens when illuminated with 540-nm light.
(b) What is the linear width (diameter) of the central maximum at the focal distance of the lens?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction60ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction60ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction60ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.61P
The resolution of a telescope is ultimately limited by the diameter of its objective lens or mirror. A typical amateur astronomer’s telescope may have a 6.0-in.-diameter mirror.
(a) What is the minimum angular separation (in arc seconds) of two stars that can be resolved with a 6.0-in. scope? (Take λ to be atthe center of the visible spectrum, about 550 run, and see Froblem 57 for the definition of an arc second.)
(b) What is the minimum distance (in km) between two points on the Moon’s surface that can be resolved by a 6.0-in. scope? (Note: The average distance from Earth to the Moon is 384,400 km.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction61ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction61ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.62P
Early cameras were little more than a box with a pinhole on the side opposite the film.
(a) What angular resolution would you expect from a pinhole with a 0.50-mm diameter?
(b) What
is the greatest distance from the camera at which two point objects 15 cm apart can be resolved? (Assume light with a wavelength of 520 nm.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction62ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction62ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.63P
A grating has 787 lines per centimeter. Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 655-nm light.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction63ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction63ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.64P
Suppose you want to produce a diffraction pattern with X-rays whose wavelength is 0.030 nm. If you use a diffraction grating, what separation between lines is needed to generate a pattern with the first maximum at an angle of 14°? (For comparison, a typical atom is a few tenths of a nanometerindiameter.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction64ps

Chapter 28 Physical Optics: Interference and Diffraction Q.65P
A diffraction grating has 2200 lines/cm. What is the angle between the first-order maxima for red light (λ = 680 nm) and blue light (λ =410 nm)?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction65ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction65ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.66P
A diffractiongrating with 345 lines/mm is 1.00 m in front of a screen. What is the wavelength of light whose first-order maxima will be 16.4 cm from the central maximum on the screen?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction66ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction66ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.67P
The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it produces a first-order principal maximum at an angle of 1.250°. Calculate the number of lines per centimeter on the grating.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction67ps

Chapter 28 Physical Optics: Interference and Diffraction Q.68P
IP The second-order maximum produced by a diffraction grating with 560 lines per centimeter is at an angle of 3.1°.
(a) What is the wavelength of the light that illuminates the grating?
(b) If a grating with a larger number of lines per centimeter is used with this light, is the angle of the second-order maximum greater than or less than 3.1°? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction68ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction68ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.69P
White light strikes a gratingwith 7600 lines/cm at normal incidence. How many complete visible spectra will be formed on either side of the central maximum? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction69ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction69ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction69ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.70P
White light strikes a diffraction grating (890 lines/mm) at normal incidence. What is the highest-order visible maximum that is formed? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction70ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction70ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.71P
White light strikes a diffraction grating (760 lines/mm) at normal incidence. What is the longest wavelength that forms a second-order maximum?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction71ps

Chapter 28 Physical Optics: Interference and Diffraction Q.72P
A light source emits two distinct wavelengths [λ1 = 430 nm (violet); λ2 = 630 nm (orange)]. The light strikes a diffraction grating with 450 lines/mm at normal incidence. Identify the colors of the first eight interference maxima on either side of the central maximum.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps2
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps3
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps4
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction72ps5

Chapter 28 Physical Optics: Interference and Diffraction Q.73P
A laser emits two wavelengths (λ1 = 420 nm; λ2 = 630 nm). When these two wavelengths strike a grating with 450 lines/mm, they produce maxima (in different orders) that coincide.
(a) What is the order (m)of each of the two overlapping lines?
(b) At what angle does this overlap occur?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction73ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction73ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.74P
IP When blue light with a wavelength of 465 nm illuminates a diffraction grating, it produce’s a first-order principal maximum but no second-order maximum.
(a) Explain the absence of higher-order principal maxima.
(b) What is the maximum spacing between lines on this grating?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction74ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction74ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.75P
Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 2.10 m away. If the first-order maxima are separated by 1.53 m on the screen, what is the distance between the two second-order maxima?
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction75ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction75ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.76P
A diffraction grating with a slit separation d is illuminated bya beam of monochromatic light of wavelength λ. The diffracted beam is observed at an angle ϕ relative to the incident direction. If the plane of the grating bisects the angle between the incident and diffracted beams, show that the mth maximum will be observed at anangle that satisfies the relation mλ = 2d sin(ϕ/2), with m = 0, ±1, ±2,….
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction76ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction76ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.77GP
CE Monochromatic light with a wavelength λ passes through a single slit of width W and forms a diffraction pattern of alternating bright and dark fringes, (a) if the width of the slit is decreased, do the dark fringes move outward or inward? Explain. (b) What width is necessary for the first dark fringe to move outward to infinity? Give your answer in terms of λ.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction77ps

Chapter 28 Physical Optics: Interference and Diffraction Q.78GP
CE Predict/Explain (a) If a thin liquid film floating on water has an index of refraction less than that of water, will the film appear bright or dark in reflected light as its thickness goes to zero? (b) Choose the best explanation from among the following:
I. The film will appear bright because as the thickness of the film goes to zero the phase difference for reflected rays goes to zero.
II. The film will appear dark because there is a phase change at both interfaces, and this will cause destructive interference of the reflected rays.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction78ps
(b)
Therefore the best explanation is I.

Chapter 28 Physical Optics: Interference and Diffraction Q.79GP
CE If the index of refraction of an eye could be magically reduced, would the eye’s resolution increase or decrease? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction79ps

Chapter 28 Physical Optics: Interference and Diffraction Q.80GP
CE In orderto increase the resolution of a camera, should its f-number be increased or decreased? Explain.
Solution:
The resolution of camera increases, when we increase the diameter of aperture of the camera. But f-number is inversely proportional to diameter. Therefore in order increase the resolution of a camera the f-numbers must be decreased.

Chapter 28 Physical Optics: Interference and Diffraction Q.81GP
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction81p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction81ps

Chapter 28 Physical Optics: Interference and Diffraction Q.82GP
When reading the printout from a laser printer, you are actually looking at an array of tiny dots. If the pupil of your eye is 4.3 mm in diameter when reading a page held 28 cm from your eye, what is the minimum separation of adjacent dots that can be resolved? (Assume light with a wavelength of 540 nm, and use 1.36 as the index of refraction for the interior of the eye.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction82ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction82ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.83GP
The headlights of a pickup truck are 1.32 m apart. What is the greatest distance at which these headlights can be resolved as separate points of light on a photograph taken with a camera whose aperture lias a diameter of 12.5 mm? (Take λ = 555 rim.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction83ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction83ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.84GP
Antireflection Coating A glass lens (nglass = 1.52) has an antireflcction coating of MgF2 (n = 1.38). (a) For 517-nm light, what minimum thickness of MgF2 will cause the reflected rays R2 and R4 in Figure 28–40 to interfere destmctively, assuming normal incidence? (b) Interference will also occur between the forward-moving rays R1 and R3 in Figure 28–40. What minimum thickness of MgF2 will cause these two rays to interfere constructively?
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction84p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction84pss
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction84pss1

Chapter 28 Physical Optics: Interference and Diffraction Q.85GP
IP White light reflected at normal incidence from a soap bubble (n = 1.33) in air produces an interference maximum at λ = 575 nm but no interference minima in the visible spectrum.
(a) Explain the absence of interferenceminima in the visible.
(b) What are the possible thicknesses of the soap film? (Refer to Example 25–3 for the range of visible wavelengths.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction85ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction85ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.86GP
A thin film of oil (n = 1.30) floats on water (n − 1.33). When sunlight is incident at right angles to this film, the only colors that are enhanced by reflection are blue (458 nm) and red (687 nm). Estimate the thickness of the oil film.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction86ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction86ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.87GP
The yellow light of sodium, with wavelengths of 588.99 nm and 589.59 nm, is normally incident on a grating with 494 lines/cm. Find the linear distance between the first-order maxima for these two wavelengths on a screen 2.55 m from the grating.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction87ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction87ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.88GP
IP A thin soap film (n = 1.33) suspended in air has a uniform thickness. When white light strikes the film at normal incidence, violet light (λv = 420 nm) is constructively reflected. (a) If we would like green light (λG = 560 nm) to be constructively reflected, instead, should the film’s thickness be increased or decreased? (b) Find the new thickness of the film. (Assume the film has the minimum thickness that can produce these reflections.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction88ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction88ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.89GP
IP A thin film of oil (n = 1.40) floats on water (n = 1.33). When sunlight is incident at right angles to this film, the only colors that are absent from the reflected light are blue (458 nm) and red (687 nm). Estimate the thickness of the oil film.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction89ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction89ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.90GP
IP Sodium light, with a wavelength of λ = 589 nm, shines downward onto the system shown in Figure 28–37. When viewed from above, you see a series of concentric circles known as Newton’s rings, (a) Do you expect a bright or a dark spot at the center of the pattern? Explain, (b) If the radius of curvature of the plano-convex lens is R = 26.1 m, what is the radius of the tenth-largest dark ring? (Only rings of nonzero radius will be counted as “rings.”)
Solution:
a) In Newton’s ring arrangement the thickness of air film at the point of contact is zero, i.e., there is no path difference between the rays reflected from upper and lower surfaces of air film. Light reflected from the lower surface of the lens has no phase change. Light reflected from the top surface of the flat glass piece undergoes half – wavelength phase change. As a result they are half a wavelength out of phase resulting in destructive interference. Hence, the center of the pattern is a dark spot.
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction90ps

Chapter 28 Physical Optics: Interference and Diffraction Q.91GP
IP Figure 28–39 shows a single-slit diffraction pattern formed by light passing througha slit of width W = 11.2 μm and illuminating a screen 0.855 m behind the slit, (a) What is the wavelength of the light? (b) If the width of the slit is decreased, will the distance indicated in Figure 28–39 be greater than or less than 15.2 cm? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction91ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction91ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction91ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.92GP
B10Entoptic Halos Images produced by structures within the eye (like lens fibers or cell fragments) are referred to as entoptic images. These images can sometimes take the form of “halos” around a bright light seen against a dark background. The halo in such a case is actually the bright outer rings of a circular diffraction pattern, like Figure 28–21, with the central bright spot not visible because it overlaps the direct image of tine light. Find the diameter of the eye structure that causes a circular diffraction pattern with the first dark ring at an angle of 3.7° when viewed with monochromatic light of wavelength 630 nm. (Typical eye structures of this type have diameters on the orderof 10 μm. Also, the index of refraction of the vitreous humor is 1.336.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction92ps

Chapter 28 Physical Optics: Interference and Diffraction Q.93GP
White light is incident on a soap film (n = 1.33, thickness = 800.0 nm) suspended in air. If the incident light makes a 45° angle with the normal to the film, what visible wavelength(s) will be constructively reflected? (Refer to Example 25-3 for the range of visible wavelengths.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction93ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction93ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction93ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.94GP
A system like that shown in Figure consists of N slits, each transmitting light of intensity I0. The light from each slit has the same phase and the same wavelength. The net intensity I observed at an angle θ due to all N slits is
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction94p
In this expression, ϕ = (2πd/λ) sin θ, where λ is the wavelength of the light, (a) Show that the intensity in the limit θ→0 is I = N2I0. This is the maximum intensity of the interference pattern, (b) Show that the first points of zero intensity on cither side of θ = 0 occur atϕ = 2π/N and ϕ = −2π/N. (c) Does the central maximum (θ = 0) of this pattern become narrower or broader as the number of slits is increased? Explain.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction94ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction94ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.95GP
Two plates of glass are separated on both ends by small wires of diameter d. Derive an expression for the condition for constructive interference when light of wavelength λ is incident normally on the plates. Consider only interference between waves reflected from the bottom of the top plate and the top of the bottom plate.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction95ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction95ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.96GP
A curved piece of glass wi th a radius of curvature R rests on a flat plate of glass. Light of wavelength A is incident normally on this system. Considering only interference between waves reflected from the curved (lower) surface of glass and the top surface of the plate, show that the radius of the nth dark ring is
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction96p
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction96ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction96ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction96ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.97GP
BIO The Resolution of the Eye The resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter ig 4.25 mm? Assume light with awavelength of λ = 550 nm. (Note: The distance from the pupil to the retina is 25.4mm. In addition, the space between the pupil and the retina is filled with a fluid whose index of refraction is n = 1.36.)
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction97ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction97ps1
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction97ps2

Chapter 28 Physical Optics: Interference and Diffraction Q.98PP
What is the minimum angle your eye can resolve, according to the Rayleigh criterion and the above assumptions?
A. 0.862 × 10−4 rad
B. 1.05 − 10−4 rad
C. 1.43 × 10−4 rad
D. 1.95 × 10−4 rad
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction98ps

Chapter 28 Physical Optics: Interference and Diffraction Q.99PP
What is the linear separation between horizontal lines on the screen?
A. 0.0235 mm
B. 0.145 mm
C. 0.369 mm
D. 0.926 mm
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction99ps

Chapter 28 Physical Optics: Interference and Diffraction Q.100PP
What is the angular separation of the horizontal lines as viewed from a distance of 12.0 feet?
A. 1.01 × 10−4 rad
B. 2.53 × 10−4 rad
C. 2.56 × 10−4 rad
D. 12.1 × 10−4 rad
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction100ps

Chapter 28 Physical Optics: Interference and Diffraction Q.101PP
According to the Rayleigh criterion, what is the closest you can be to the TV screen before resolvingthe individual horizontal lines? (In practice you can be considerably closer than this distance before resolving the lines.)
A. 3.51 ft
B. 4.53 ft
C. 11.5 ft
D. 14.0 ft
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction101ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction101ps1

Chapter 28 Physical Optics: Interference and Diffraction
IP Referring to Example 28–2 Suppose we change the slit separation to a value other than 8.5 × 10−5m, with the result that the linear distance to the tenth bright fringe above the central bright fringe increases from 12 cm to 18 cm. The screen is still 2.3 m from the slits, and the wavelength of the light is 440 nm. (a) Did we increase or decrease the slit separation? Explain, (b) Find the new slit separation.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction102ps
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction102ps1

Chapter 28 Physical Optics: Interference and Diffraction Q.103IP
IP Referring to Example 28–2 The wavelength of the light is changed to a value other than 440 nm, with the result that the linear distance to the seventh bright fringe above the central, bright fringe is 12 cm. The screen is still 2.3 m from the slits, and the slit separation is 8.5 × 10−5 m. (a) Is the new wavelength longer or shorter than 440 nm? Explain, (b) Find the new wavelength.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction103ps

Chapter 28 Physical Optics: Interference and Diffraction Q.104IP
IP Referring to Example 28–5 The light used in this experiment has a wavelength of 511 nm. (a) If the width of the slit is decreased, will the angle to the first dark fringe above the central bright fringe increase or decrease? Explain, (b) Find the angle to the first dark fringe if the reduced slit width is 1.50 × 10−6 m.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction104ps

Chapter 28 Physical Optics: Interference and Diffraction Q.105IP
IP Referring to Example 28–5 The width of the slit in this experiment is 2.20 × 10−6 m. (a) If the frequency of the light is decreased, will the angle to the first dark fringe above the central bright fringe increase or decrease? Explain, (b) Find the angle to the first dark fringe if the reduced frequency is 5.22 × 1014 Hz.
Solution:
mastering-physics-solutions-chapter-28-physical-optics-interference-and-diffraction105ps

Mastering Physics Solutions Chapter 27 Optical Instruments

Mastering Physics Solutions Chapter 27 Optical Instruments

Mastering Physics Solutions

Chapter 27 Optical Instruments Q.1CQ
Why is it restful to your eyes to gaze off into the distance?
Solution:
When a person with normal vision relaxes the cilliary muscles of the eye. An object at infinity is in focus. In a nearsighted person , however , a totally relaxed eye focuses only out to a finite distance from the eye- the far point. Thus a person with condition is said to be nearsighted because objects near the eye can be focused , where as objects beyond the far point are fuzzy.

Chapter 27 Optical Instruments Q.1P
· CEPredict/Explain BIO Octopus Eyes To focus its eyes, an octopus does not change the shape of its lens, as is the case in humans. Instead, an octopus moves its rigid lens back and forth, as in a camera. This changes the distance from the lens to the retina and brings an object into focus. (a) If an object moves closer to an octopus, must the octopus move its lens closer to or farther from its retina to keep the object in focus? (b) Choose the best explanation from among the following:
I. The lens must move closer to the retina—that is, farther away from the object—to compensate for the object moving closer to the eye.
II. When the object moves closer to the eye, the image produced by the lens will be farther behind the lens; therefore, the lens must move farther from the retina.
Solution:
(a) To focus its eyes, an octopus does not change the shape of its lens, as in the case in humans. Instead, an octopus moves its rigid lens back and forth, as in a camera. This changes the distance from the lens to the retina and brings an object into focus.
If an object moves closer to an octopus, the image produced by the lens will be farther behind the lens. Therefore, in order to keep the object in focus, the octopus must move its lens farther from its retina.
(b) The correct explanation is option (II).
Option (II): When the object moves closer to the eye, the image produced by the lens will be farther behind the lens; therefore, the lens must move farther from the retina.

Chapter 27 Optical Instruments Q.2CQ
If a lens is cut in half through a plane perpendicular to its surface, does it show only half an image?
Solution:
No, when the lens is cut into half through plane perpendicular to its surface the focal length lens remains the same. So, the lens now shows the same image.

Chapter 27 Optical Instruments Q.2P
Your friend is 1.9 m tall. (a) When she stands 3.2 m from you, what is the height of her image formed on the retina of your eye? (Consider the eye to consist of a thin lens 2.5 cm from the retina.) (b) What is the height of her image when she is 4.2 m from you?
Solution:
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mastering-physics-solutions-chapter-27-optical-instruments2ps1

Chapter 27 Optical Instruments Q.3CQ
If your near-point distance is N, how close can you stand to a mirror and still be able to focus on your image?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments3cqs

Chapter 27 Optical Instruments Q.3P
Which forms the larger image on the retina of your eye: a 43-ft tree seen from a distance of 210 ft, or a 12-in. flower viewed from a distance of 2.0 ft?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments3ps
mastering-physics-solutions-chapter-27-optical-instruments3ps1

Chapter 27 Optical Instruments Q.4CQ
When you open your eyes underwater, everything looks blurry. Can this be thought of as an extreme case of nearsightedness or farsightedness? Explain.
Solution:
It looks blurry under water because there will be less refraction of light. When it passes from water to your cornea than when it passes from air to your cornea. Therefore, your eyes simply aren’t converging light enough when they are in water. Since if your eyes do not converge light as much as they can then we can say farsighted ness is caused.
mastering-physics-solutions-chapter-27-optical-instruments4cqs

Chapter 27 Optical Instruments Q.4P
Approximating the eye as a single thin lens 2.60 cm from the retina, find the eye’s near-point distance if the smallest focal length the eye can produce is 2.20 cm.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments4ps

Chapter 27 Optical Instruments Q.5CQ
Would you benefit more from a magnifying glass if your nearpoint distance is 25 cm or if it is 15 cm? Explain.
Solution:
A person with the larger near-point distance benefits more from the magnifier. Since a person with the smaller near-point distance can examine an object at closer range than a person with the larger near-point distance.

Chapter 27 Optical Instruments Q.5P
Referring to Problem 4, what is the focal length of the eye when it is focused on an object at a distance of (a) 285 cm and (b) 28.5 cm?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments5ps
mastering-physics-solutions-chapter-27-optical-instruments5ps1

Chapter 27 Optical Instruments Q.6CQ
When you use a simple magnifying glass, does it matter whether you hold the object to be examined closer to the lens than its focal length or farther away? Explain.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments6cqs
Yes, it matters; a simple magnifier is nothing more than a convex lens.
From the above figures we can say that a convex lens forms the images enlarged only when the object is closer to the lens than its focal lengths.

Chapter 27 Optical Instruments Q.6P
mastering-physics-solutions-chapter-27-optical-instruments6p
Solution:
mastering-physics-solutions-chapter-27-optical-instruments6ps
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Chapter 27 Optical Instruments Q.7CQ
Is the final image produced by a telescope real or virtual? Explain.
Solution:
The image formed by the objective is essentially at the focal point of the eye-piece. This means the eyepiece forms a virtual image at infinity that the observer can view with a relaxed eye.
mastering-physics-solutions-chapter-27-optical-instruments7cqs
mastering-physics-solutions-chapter-27-optical-instruments7cqs1

Chapter 27 Optical Instruments Q.7P
BIO The focal length of the human eye is approximately 1.7 cm. (a) What is the f-number for the human eye in bright light, when the pupil diameter is 2.0 mm? (b) What is the f-number in dim light, when the pupil diameter has expanded to 7.0 mm?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments7ps

Chapter 27 Optical Instruments Q.8CQ
Does chromatic aberration occur in mirrors? Explain.
Solution:
No, because the image formed by a mirror is due to the reflection of light, but not the refraction of light. Chromatic aberration occurs in lenses because of refraction of different colors of light. Since the reflection of light does not depends on color, the light of all colors bent in the same way by a mirror; therefore there will be no chromatic aberration in the case of mirror.

Chapter 27 Optical Instruments Q.8P
IP A camera with a 55-mm-focal-length lens has aperture settings of 2.8, 4, 8, 11, and 16. (a) Which setting has the largest aperture diameter? (b) Calculate the five possible aperture diameters for this camera.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments8ps
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Chapter 27 Optical Instruments Q.9P
The actual frame size of “35-mm” film is 24 mm × 36 mm. You want to take a photograph of your friend, who is 1.9 m tall. Your camera has a 55-mm-focal-length lens. How far from the camera should your friend stand in order to produce a 36-mm- tall image on the film?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments9ps
mastering-physics-solutions-chapter-27-optical-instruments9ps1

Chapter 27 Optical Instruments Q.10P
To completely fill a frame of “35-mm” film, the image produced by a camera must be 36 mm high. If a camera has a focal length of 150 mm, how far away must a 2.0-m-tall person stand to produce an image that fills the frame?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments10ps
mastering-physics-solutions-chapter-27-optical-instruments10ps1

Chapter 27 Optical Instruments Q.11P
· · You are taking a photograph of a poster on the wall of your dorm room, so you can’t back away any farther than 3.0 m to take the shot. Tire poster is 0.80 m wide and 1.2 m tall, and you want the image to fit in the 24-mm × 36-mm frame of the film in your camera. What is the longest focal length lens that will work?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments11ps

Chapter 27 Optical Instruments Q.12P
A photograph is properly exposed when the aperture is set to f/8 and the shutter speed is 125. Find the approximate shutter speed needed to give the same exposure if the aperture is changed to f/2.4.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments12ps
mastering-physics-solutions-chapter-27-optical-instruments12ps1

Chapter 27 Optical Instruments Q.13P
You are taking pictures of the beach at sunset. Just before the Sun sets, a shutter speed of f/11 produces a properly exposed picture. Shortly after the Sun sets, however, your light meter indicates that the scene is only one-quarter as bright as before. (a) If you don’t change the aperture, what approximate shutter speed is needed for your second shot? (b) If, instead, you keep the shutter speed at 1/100 s, what approximate f-stop will be needed for the second shot?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments13ps
mastering-physics-solutions-chapter-27-optical-instruments13ps1

Chapter 27 Optical Instruments Q.14P
· · IP You are taking a photograph of a horse race. A shutter speed of 125 at f/5.6 produces a properly exposed image, but the running horses give a blurred image. Your camera has f-stops of 2, 2.8, 4, 5.6, 8, 11, and 16. (a) To use the shortest possible exposure time (i.e., highest shutter speed), which f-stop should you use? (b) What is the shortest exposure time you can use and still get a properly exposed image?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments14ps
mastering-physics-solutions-chapter-27-optical-instruments14ps1

Chapter 27 Optical Instruments Q.15P
The Hale Telescope The 200-in. (5.08-m) diameter mirror of the Hale telescope on Mount Palomar has a focal length ƒ = 16.9 m. (a) When the detector is placed at the focal point of the mirror (the “prime focus”), what is the f-ratio for this telescope? (b) The coudé focus arrangement uses additional mirrors to bend the light path and increase the effective focal length to 155.4 m. What is the f-ratio of the telescope when the coudé focus is being used? (Coudé is French for “elbow,” since the light path is “bent like an elbow.” This arrangement is useful when the light needs to be focused onto a distant instrument.)
Solution:
mastering-physics-solutions-chapter-27-optical-instruments15ps

Chapter 27 Optical Instruments Q.16P
· CEPredict/Explain Two professors arc stranded on a deserted island. Both wear glasses, though one is nearsighted and the other is farsighted. (a) Which person’s glasses should be used to focus the rays of the Sun and start a fire? (b) Choose the best explanation from among the following:
I. A nearsighted person can focus close, so that person’s glasses should be used to focus the sunlight on a piece of moss at a distance of a couple inches.
II. A farsighted person can’t focus close, so the glasses to correct that person’s vision are converging. A converging lens is what you need to concentrate the rays of the Sun.
Solution:
1403-27-16P SA Code: 6078.
SR Code:5784
(a). We know that the farsighted person uses converging glasses. The convex lens focuses light from an object inside near point to produce an image that is beyond the near point. Therefore the farsighted person’s glasses are used to start the fire.
(b)Therefore the best explanation is II

Chapter 27 Optical Instruments Q.17P
· CE A clerk at the local grocery store wears glasses that make her eyes look larger than they actually are. Is the clerk nearsighted or farsighted? Explain.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments17ps

Chapter 27 Optical Instruments Q.18P
CE The umpire at a baseball game wears glasses that make his eyes look smaller than they actually are. Is the umpire nearsighted or farsighted? Explain.
Solution:
By wearing diverging lens the eyes appear smaller than the actual one. If the Umpire wears diverging lens then he should be nearsighted.

Chapter 27 Optical Instruments Q.19P
Construct a ray diagram for Active Example 27–2.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments19ps
mastering-physics-solutions-chapter-27-optical-instruments19ps1

Chapter 27 Optical Instruments Q.20P
The cornea of a normal human eye has an optical power of +43.0 diopters. What is its focal length?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments20ps

Chapter 27 Optical Instruments Q.21P
A myopic student is shaving without his glasses. If Iris eyes have a far point of 1.6 m, what is the greatest distance he can stand from the mirror and still see his image clearly?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments21ps
mastering-physics-solutions-chapter-27-optical-instruments21ps1

Chapter 27 Optical Instruments Q.22P
An eyeglass prescription calls for a lens with an optical power of +2.7 diopters. What is the focal length of this lens?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments22ps

Chapter 27 Optical Instruments Q.23P
Two thin lenses, with f1 = +25.0 cm and f2 = —42.5 cm, are placed hr contact. What is the focal length of this combination?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments23ps

Chapter 27 Optical Instruments Q.24P
Two thin lenses have refractive powers of +4.00 diopters and —2.35 diopters. What is the refractive power of the two if they are placed in contact? (Note that these are the same two lenses described in the previous problem.)
Solution:
mastering-physics-solutions-chapter-27-optical-instruments24ps
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mastering-physics-solutions-chapter-27-optical-instruments24ps2

Chapter 27 Optical Instruments Q.25P
Two concave lenses, each with ƒ = —12 cm, are separated by 6.0 cm. An object is placed 24 cm in front of one of the lenses. Find (a) the location and (b) the magnification of the final image produced by this lens combination.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments25ps
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Chapter 27 Optical Instruments Q.26P
IP BIO The focal length of a relaxed human eye is approximately 1.7 cm. When we focus our eyes on a close-up object, we can change the refractive power of the eye by about 16 diopters. (a) Does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? Explain. (b) Calculate the focal length of the eye when we focus closely.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments26ps

Chapter 27 Optical Instruments Q.27P
IP BIO Diopter Change in Diving Cormorants Double- crested cormorants (Phalacrocorax auritus) are extraordinary birds—they can focus on objects in the air, just like we can, but they can also focus underwater as they pursue their prey. To do so, they have one of the largest accommodation ranges in nature— that is, they can change the focal length of their eyes by amounts that are greater than is possible in other animals. When a cormorant plunges into the ocean to catch a fish, it can change the refractive power of its eyes by about 45 diopters, as compared to only 16 diopters of change possible in the human eye. (a) Should this change of 45 diopters be an increase or a decrease? Explain. (b) If the focal length of the cormorant’s eyes is 4.2 mm before it enters the water, what is the focal length after the refractive power changes by 45 diopters?
Solution:
mastering-physics-solutions-chapter-27-optical-instruments27ps

Chapter 27 Optical Instruments Q.28P
A converging lens of focal length 8.000 cm is 20.0 cm to the left of a diverging lens of focal length –6.00 cm. A coin is placed 12.0 cm to the left of the converging lens. Find (a) the location and (b) the magnification of the coin’s final image.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments28ps
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Chapter 27 Optical Instruments Q.29P
Repeat Problem 28, this time with the coin placed 18.0 cm to the right of the diverging lens.
Solution:
mastering-physics-solutions-chapter-27-optical-instruments29ps
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Chapter 27 Optical Instruments Q.30P
Find the focal length of contact lenses that would allow a farsighted person with a near-point distance of 176 cm to read a book at a distance of 10.1 cm.
Solution:
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Chapter 27 Optical Instruments Q.31P
Find the focal length of contact lenses that would allow a nearsighted person with a 135-cm far point to focus on the stars at night.
Solution:
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Chapter 27 Optical Instruments Q.32P
What focal length should a pair of contact lenses have if they are to correct the vision of a person with a near point of 56 cm?
Solution:
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Chapter 27 Optical Instruments Q.33P
A nearsighted person wears contacts with a focal length of –8.5 cm. Tf this person’s far-point distance with her contacts is 8.5 m, what is her uncorrected far-point distance?
Solution:
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Chapter 27 Optical Instruments Q.34P
Without Iris glasses, Isaac can see objects clearly only if they are less than 4.5 m from his eyes. What focal length glasses worn 2.1 cm from his eyes will allow Isaac to see distant objects clearly?
Solution:
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Chapter 27 Optical Instruments Q.35P
A person whose near-point distance is 49 cm wears a pair of glasses that are 2.0 cm from her eyes. With the aid of these glasses, she can now focus on objects 25 cm away from her eyes. Find the focal length and refractive power of her glasses.
Solution:
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Chapter 27 Optical Instruments Q.36P
A pair of eyeglasses is designed to allow a person with a far- point distance of 2.50 m to read a road sign at a distance of 25.0 m. Find the focal length required of these glasses if they are to be worn (a) 2.00 cm or (b) 1.00 cm from the eyes.
Solution:
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Chapter 27 Optical Instruments Q.37P
IP Your favorite aunt can read a newspaper only if it is within 15.0 cm of her eyes. (a) Is your aunt nearsighted or farsighted? Explain. (b) Should your aunt wear glasses that are converging or diverging to improve her vision? Explain. (c) How many diopters of refractive power must her glasses have if they are worn 2.00 cm from the eyes and allow her to read a newspaper at a distance of 25.0 cm?
Solution:
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Chapter 27 Optical Instruments Q.38P
IP The relaxed eyes of a patient have a refractive power of
48.5 diopters. (a) Is this patient nearsighted or farsighted? Explain. (b) If this patient is nearsighted, find the far point. If this person is farsighted, find the near point. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)
Solution:
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Chapter 27 Optical Instruments Q.39P
IP You are comfortably reading a book at a distance of 24 cm. (a) What is the refractive power of your eyes? (b) Does the refractive power of your eyes increase or decrease when you move the book farther away? Explain. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)
Solution:
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Chapter 27 Optical Instruments Q.40P
Without glasses, your Uncle Albert can sec things clearly only if they are between 25 cm and 170 cm from his eyes. (a) What power eyeglass lens will correct your uncle’s myopia? Assume the lenses will sit 2.0 cm from his eyes. (b) What is your uncle’s near point when wearing these glasses?
Solution:
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Chapter 27 Optical Instruments Q.41P
A 2.05-cm-tall object is placed 30.0 cm to the left of a converging lens with a focal length f1 = 20.5 cm. A diverging lens, with a focal length f2 = –42.5 cm, is placed 30.0 cm to the right of the first lens. How tall is the final image of the object?
Solution:
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Chapter 27 Optical Instruments Q.42P
A simple camera telephoto lens consists of two lenses. The objective lens has a focal length f1 = +39.0 cm. Precisely 36.0 cm behind this lens is a concave lens with a focal length f2 = –10.0 cm. The object to be photographed is 4.00 m in front of the objective lens. (a) How far behind the concave lens should the film be placed? (b) What is the linear magnification of this lens combination?
Solution:
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Chapter 27 Optical Instruments Q.43P
IP With unaided vision, a librarian can focus only on objects that lie at distances between 5.0 m and 0.50 m. (a) Which type of lens (converging or diverging) is needed to correct his nearsightedness? Explain. (b) Which type of lens will correct his farsightedness? Explain. (c) Find the refractive power needed for each part of the bifocal eyeglass lenses that will give the librarian normal visual acuity from 25 cm out to infinity. (Assume the lenses rest 2.0 cm from his eyes.)
Solution:
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Chapter 27 Optical Instruments Q.44P
IP With unaided vision, a physician can focus only on objects that lie at distances between 5.0 m and 0.50 m. (a) Which type of lens (converging or diverging) is needed to correct her nearsightedness? Explain. (b) Which type of lens will correct her farsightedness? Explain. (c) Find the refractive power needed for each part of the bifocal contact lenses that will give the physician normal visual acuity from 25 cm out to infinity.
Solution:
The physician can focus only on objects that lie at distances between 5.0 m and 0.50 m.so physician has nearsightedness.
(a)
In a nearsighted a person, however, a totally relaxed eyes focuses only out to a finite distance from the eye. Thus a person with this condition is said to be nearsighted because objects near the eye can be focused.
The diverging lens can produce an image of a distant object at physician far point distance, so, the physician should wear glasses with diverging lenses.
(b)
A Converging lens in front of the eye can correct for farsightedness. The convex lens focuses light from an object inside the near point to produce an image that is beyond the near point. The eye can now focus on the image of the object.
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Chapter 27 Optical Instruments Q.45P
A person’s prescription for her new bifocal glasses calls for a refractive power of –0.445 diopter in the distance-vision part, and a power of +1.85 diopters in the close-vision part. What are the near and far points of this person’s uncorrected vision? Assume the glasses are 2.00 cm from the person’s eyes, and that the person’s near-point distance is 25.0 cm when wearing the glasses.
Solution:
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Chapter 27 Optical Instruments Q.46P
A person’s prescription for his new bifocal eyeglasses calls for a refractive power of –0.0625 diopter in the distance-vision part and a power of +1.05 diopters in the close-vision part. Assuming the glasses rest 2.00 cm from Iris eyes and that the corrected near-point distance is 25.0 cm, determine the near and far points of this person’s uncorrected vision.
Solution:
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Chapter 27 Optical Instruments Q.47P
Two lenses, with f1 = +20.0 cnr and f2 = +30.0 cm, are placed on the x axis, as shown in Figure 27-22. An object is fixed 50.0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to lens 2 for the following cases: (a) x = 115 cm; (b) x = 30.0 cm; (c) x = 0. (d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, 1/feff = l/f1 + 1/f2.
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Solution:
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Chapter 27 Optical Instruments Q.48P
A converging lens with a focal length of 4.0 cm is to the left of a second identical lens. When a feather is placed 12 cm to the left of the first lens, the final image is the same size and orientation as the feather itself. What is the separation between the lenses?
Solution:
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Chapter 27 Optical Instruments Q.49P
The Moon is 3476 km in diameter and orbits the Earth at an average distance of 384,400 km. (a) What is the angular size of the Moon as seen from Earth? (b) A penny is 19 mm in diame- ter. How far from your eye should the penny be held to produce the same angular diameter as the Moon?
Solution:
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Chapter 27 Optical Instruments Q.50P
A magnifying glass is a single convex lens with a focal length of ƒ = +14.0 cm. (a) What is the angular magnification when this lens forms a (virtual) image at —∞? How far from the object should the lens be held? (b) What is the angular magnification when this lens forms a (virtual) image at the person’s near point (assumed to be 25 cm)? How far from the object should the lens be held in this case?
Solution:
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Chapter 27 Optical Instruments Q.51P
IP A student has two lenses, one of focal length f1 = 5.0 cm and the other with focal length f2 = 13 cm. (a) When used as a simple magnifier, which of these lenses can produce the greater magnification? Explain, (b) Find the maximum magnification produced by each of these lenses.
Solution:
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Chapter 27 Optical Instruments Q.52P
A beetle 4.73 mm long is examined with a simple magnifier of focal length f = 10.1 cm. If the observer’s eye is relaxed while using the magnifier, and has a near-point distance of 25.0 cm, what is the apparent length of the beetle?
Solution:
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Chapter 27 Optical Instruments Q.53P
To engrave wishes of good luck on a watch, an engraver uses a magnifier whose focal length is 8.65 cm. If the image formed by the magnifier is at the engraver’s near point of 25.6 cm, find (a) the distance between the watch and the magnifier and (b) the angular magnification of the engraving. Assume the magnifying glass is directly in front of the engraver’s eyes.
Solution:
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Chapter 27 Optical Instruments Q.54P
A jeweler examines a diamond with a magnifying glass. If the near-point distance of the jeweler is 20.8 cm, and the focal length of the magnifying glass is 7.50 cm, find the angular magnification when the diamond is held at the focal point of the magnifier. Assume the magnifying glass is directly in front of the jeweler’s eyes.
Solution:
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Chapter 27 Optical Instruments Q.55P
in Problem 54, find the angular magnification when the diamond is held 5.59 cm from the magnifying glass.
Solution:
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Chapter 27 Optical Instruments Q.56P
A person with a near-point distance of 25 cm finds that a magnifying glass gives an angular magnification that is 1.5 times larger when the image of the magnifier is at the near point than when the image is at infinity. What is the focal length of the magnifying glass?
Solution:
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Chapter 27 Optical Instruments Q.57P
CE You have two lenses: lens 1 with a focal length of 0.45 cm and lens 2 with a focal length of 1.9 cm. If you construct a microscope with these lenses, which one should you use as the objective? Explain.
Solution:
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Chapter 27 Optical Instruments Q.58P
A compound microscope has an objective lens with a focal length of 2.2 cm and an eyepiece with a focal length of 5.4 cm. If the image produced by the objective is 12 cm from the objective, what magnification does this microscope produce?
Solution:
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Chapter 27 Optical Instruments Q.59P
BIO A typical red blood cell subtends an angle of only 1.9 × 10–5 rad when viewed at a person’s near-point distance of 25 cm. Suppose a red blood cell is examined with a compound microscope in which the objective and eyepiece are separated by a distance of 12.0 cm. Given that the focal length of the eyepiece is 2.7 cm, and the focal length of the objective is 0.49 cm, find the magnitude of the angle subtended by the red blood cell when viewed through this microscope.
Solution:
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Chapter 27 Optical Instruments Q.60P
The medium-power objective lens in a laboratory microscope has a focal length fobjective = 4.00 mm. (a) If this lens produces a lateral magnification of –40.0, what is its “working distance”; that is, what is the distance from the object to the objective lens? (b) What is the focal length of an eyepiece lens that will provide an overall magnification of 125?
Solution:
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Chapter 27 Optical Instruments Q.61P
A compound microscope has the objective and eyepiece mounted in a tube that is 18.0 cm long. The focal length of the eyepiece is 2.62 cm, and the near-point distance of the person using the microscope is 25.0 cm. If the person can view the image produced by the microscope with a completely relaxed eye, and the magnification is –4525, what is the focal length of the objective?
Solution:
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Chapter 27 Optical Instruments Q.62P
In Problem 61, what is the distance between the objective lens and the object to be examined?
Solution:
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Chapter 27 Optical Instruments Q.63P
The barrel of a compound microscope is 15 cm in length. The specimen will be mounted 1.0 cm from the objective, and the eyepiece has a 5.0-cm focal length. Determine the focal length of the objective lens.
Solution:
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Chapter 27 Optical Instruments Q.64P
A compound microscope uses a 75.0-mm lens as the objective and a 2.0-cm lens as the eyepiece. The specimen will be mounted 122 mm from the objective. Determine (a) the barrel length and (b) the total magnification produced by the microscope.
Solution:
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Chapter 27 Optical Instruments Q.65P
The “tube length” of a microscope is defined to be the difference between the (objective) image distance and objective focal length: L = di – fobjective. Many microscopes are standardized to a tube length of L = 160 mm. Consider such a microscope whose objective lens has a focal length fobjective = 7.50 mm. (a) How far from the object should this lens be placed? (b) What focal length eyepiece would give an overall magnification of –55? (c) What focal length eyepiece would give an overall magnification of –110?
Solution:
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Chapter 27 Optical Instruments Q.66P
CE Two telescopes of different length produce the same angular magnification. Is the focal length of the long telescope’s eyepiece greater than or less than the focal length of the short telescope’s eyepiece? Explain.
Solution:
The angular magnification is the ratio between focal length of the objective to the focal length of the eye piece. Now the angular magnification for both the telescopes is same, and also given that the length of one telescope is greater than the other, by considering the above two conditions we can say that the focal lengths of eye piece and objective are greater in longer telescope

Chapter 27 Optical Instruments Q.67P
CE To construct a telescope, you are given a lens with a focal length of 32 mm and a lens with a focal length of 1600 mm. (a) On the basis of focal length alone, which lens should be the objective and which the eyepiece? Explain. (b) What magnification would this telescope produce?
Solution:
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Chapter 27 Optical Instruments Q.68P
A grade school student plans to build a 35-power telescope as a science fair project. She starts with a magnifying glass with a focal length of 5.0 cm as the eyepiece. What focal length is needed for her objective lens?
Solution:
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Chapter 27 Optical Instruments Q.69P
A 55-power refracting telescope has an eyepiece with a focal length of 5.0 cm. How long is the telescope?
Solution:
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Chapter 27 Optical Instruments Q.70P
An amateur astronomer wants to build a small refracting telescope. The only lenses available to him have focal lengths of 5.00 cm, 10.0 cm, 20.0 cm, and 30.0 cm. (a) What is the greatest magnification that can be obtained using two of these lenses? (b) How long is the telescope with the greatest magnification?
Solution:
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Chapter 27 Optical Instruments Q.71P
A pirate sights a distant ship with a spyglass that gives an angular magnification of 22. If the focal length of the eyepiece is 11 mm, what is the focal length of the objective?
Solution:
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Chapter 27 Optical Instruments Q.72P
A telescope has lenses with focal lengths f1 = +30.0 cm and f2 = +5.0 cm. (a) What distance between the two lenses will allow the telescope to focus on an infinitely distant object and produce an infinitely distant image? (b) What distance between the lenses will allow the telescope to focus on an object that is 5.0 m away and to produce an infinitely distant image?
Solution:
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Chapter 27 Optical Instruments Q.73P
Jason has a 25-power telescope whose objective lens has a focal length of 120 cm. To make his sister appear smaller than normal, he turns the telescope around and looks through the objective lens. What is the angular magnification of his sister when viewed through the “wrong” end of the telescope?
Solution:
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Chapter 27 Optical Instruments Q.74P
Roughing It with Science A professor shipwrecked on Hooligan’s Island decides to build a telescope from his eyeglasses and some coconut shells. Fortunately, the professor’s eyes require different prescriptions, with the left lens having a power of +5.0 diopters and the right lens having a power of +2.0 diopters. (a) Which lens should he use as the objective? (b) What is the angular magnification of the professor’s telescope?
Solution:
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Chapter 27 Optical Instruments Q.75P
Galileo’s Telescope Galileo’s first telescope used a convex objective lens with a focal length ƒ = 1.7 m and a concave eyepiece, as shown in Figure 27-23. When this telescope is focused on an infinitely distant object, and produces an infinitely distant image, its angular magnification is +3.0. (a) What is the focal length of the eyepiece? (b) How far apart are the two lenses?
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Solution:
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Chapter 27 Optical Instruments Q.76P
The Moon has an angular size of 0.50° when viewed with unaided vision from Earth. Suppose the Moon is viewed through a telescope with an objective whose focal length is 53 cm and an eyepiece whose focal length is 25 mm. What is the angular size of the Moon as seen through this telescope?
Solution:
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Chapter 27 Optical Instruments Q.77P
In Problem 76, an eyepiece is selected to give the Moon an angular size of 15°. What is the focal length of this eyepiece?
Solution:
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Chapter 27 Optical Instruments Q.78P
A telescope is 275 mm long and has an objective lens with a focal length of 257 mm. (a) What is the focal length of the eyepiece? (b) What is the magnification of this telescope?
Solution:
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Chapter 27 Optical Instruments Q.79GP
CE Predict/Explain BIO Intracorneal Ring An intracomeal ring is a small plastic device implanted in a person’s cornea to change its curvature. By changing the shape of the cornea, the intracorneal ring can correct a person’s vision. (a) If a person is nearsighted, should the ring increase or decrease the cornea’s curvature? (b) Choose the best explanation from among the following:
I. The intracorneal ring should increase the curvature of the cornea so that it bends light more. This will allow it to focus on light coming from far away.
II. The intracorneal ring should decrease the curvature of the cornea so it’s flatter and bends light less. This will allow parallel rays from far away to be focused.
Solution:
1403-27-79GP SA: 6078
SR: 5784
RID: 267
Picture the problem:
An intra-corneal ring is a small plastic device implanted in a person’s cornea to change its curvature, and then we can correct a person’s vision.
Strategy:
A nearsighted person’s eye converges the light coming into short distance, that is, the focal length of the eye is less than the distance from lens to the retina. When a person sees that an object at infinity forms an image in front of the retina, because of the elongation of the eye.
To correct this condition, we need to undo some of the excess convergence produced by the eye, so that the final image falls on the retina.
Solution:
(a) If a person is near sighted, placing the intra-corneal ring should decrease the cornea’s curvature, so that focal length of the eye is equal to the distance from lens to the retina. Because to focus on far objects, the focal length (or radius of curvature) should be larger hence the curvature of the lens that is cornea should be smaller.
(b) Therefore the best explanation is II.
The intra-corneal ring should decrease the curvature of the cornea so it flattens and bends light less. This allows parallel rays from far away to be focused.

Chapter 27 Optical Instruments Q.80GP
· CE BIO The lens in a normal human eye, with aqueous humor on one side and vitreous humor on the other side, has a refractive power of 15 diopters. Suppose a lens is removed from an eye and surrounded by air. In this case, is its refractive power greater than, less than, or equal to 15 diopters? Explain.
Solution:
We know that the refractive index of air is less than the refractive index of any medium. If we consider the lens is placed in air, the light rays will bend more in air than in aqueous or vitreous medium.
This is because the difference in index of refraction between air and lens is greater than the difference between index of refraction of any medium other than air and the lens.
The light rays refract more when the lens is placed in air. Therefore the refractive power of the lens in air is greater than 15 diopters.

Chapter 27 Optical Instruments Q.81GP
CE An optical system consists of two lenses, one with a focal length of 0.50 cm and the other with a focal length of 2.3 cm. If the separation between the lenses is 12 cm, is the instrument a microscope or a telescope? Explain.
Solution:
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Chapter 27 Optical Instruments Q.82GP
CE Air optical system consists of two lenses, one with a focal length of 50 cm and the other with a focal length of 2.5 cm. If the separation between the lenses is 52.5 cm, is the instrument a microscope or a telescope? Explain.
Solution:
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Chapter 27 Optical Instruments Q.83GP
CE Predict/Explain BIO Treating Cataracts When the lens in a person’s eye becomes clouded by a cataract, the lens can be removed with a process called phacoemulsification and replaced with a man-made intraocular lens. The intraocular lens restores clear vision, but its focal length cannot be changed to allow the user to focus at different distances. In most cases, the intraocular lens is adjusted for viewing of distant objects, and corrective glasses are worn when viewing nearby objects. (a) Should the refractive power of the corrective glasses be positive or negative? (b) Choose the best explanation from among the following:
I. The refractive power should be positive—converging— because the intraocular lens will make the person farsighted.
II. A negative refractive power is required to bring the focal point of the intraocular lens in from infinity to a finite value.
Solution:
1403-27-83GP SA Code: 6078.
SR Code: 5784
(a)
Refractive power of corrective glasses should be positive. Because to view nearby objects, converging lenses (power is positive) are needed as the intraocular lens can not change its focal length to allow the user to focus at closer distances.
(b)
Therefore the best explanation is I

Chapter 27 Optical Instruments Q.84GP
IP Tire greatest refractive power a patient’s eyes can produce is 44.1 diopters. (a) Is this patient nearsighted or farsighted? Explain. (b) If this patient is nearsighted, find the far point. If this person is farsighted, find the near point. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)
Solution:
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Chapter 27 Optical Instruments Q.85GP
IP You are observing a rare species of bird in a distant tree with your unaided eyes. (a) What is the refractive power of your eyes? (b) Does the refractive power of your eyes increase or decrease when you shift your view to the guidebook in your hands? Explain. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)
Solution:
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Chapter 27 Optical Instruments Q.86GP
Galileo’s original telescope (Figure 27–23) used a convex objective and a concave eyepiece. Use a ray diagram to show that this telescope produces an upright image when a distant object is being viewed. Assume that the eyepiece is to the right of the object and that the right-hand focal point of the eyepiece is just to the left of the objective’s right-hand focal point. hr addition, assume that the focal length of the eyepiece has a magnitude that is about one-quarter the focal length of the objective.
Solution:
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Chapter 27 Optical Instruments Q.87GP
IP For each of the following cases, use a ray diagram to show that the angular sizes of tire image and the object are identical if both angles are measured from the center of the lens. (a) A convex lens with the object outside the focal length. (b) A convex lens with the object inside the focal length. (c) A concave lens with the object outside the focal length. (d) Given that the angular size does not change, how does a simple magnifier work? Explain.
Solution:
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Chapter 27 Optical Instruments Q.88GP
IP You have two lenses, with focal lengths f1 = +2.60 cm and f2 = +20.4 cm. (a) How would you arrange these lenses to form a magnified image of the Moon? (b) What is the maximum angular magnification these lenses could produce? (c) How would you arrange the same two lenses to form a magnified image of an insect? (d) If you use the magnifier of part (c) to view an insect, what is the angular magnification when the insect is held 2.90 cm from the objective lens?
Solution:
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Chapter 27 Optical Instruments Q.89GP
BIO Tire eye is actually a multiple-lens system, but we can approximate it with a single-lens system for most of our purposes. When the eye is focused on a distant object, the optical power of the equivalent single lens is +41.4 diopters. (a) What is the effective focal length of the eye? (b) How far in front of the retina is this “equivalent lens” located?
Solution:
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Chapter 27 Optical Instruments Q.90GP
BIO Fitting Contact Lenses with a Keratometer When a patient is being fitted with contact lenses, the curvatrue of the patient’s cornea is measured with an instrument known as a keratometer. A lighted object is held near the eye, and the keratometer measures the magnification of the image formed by reflection from the front of the conrea. If an object is held 10.0 cm in front of a patient’s eye, and the reflected image is magnified by a factor of 0.035, what is the radius of curvature of the patient’s cornea?
Solution:
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Chapter 27 Optical Instruments Q.91GP
Pricey Stamp A rare 1918 “Jenny” stamp, depicting a misprinted, upside-down Curtiss JN-4 “Jenny” airplane, sold at auction for $525,000. A collector uses a simple magnifying glass to examine the “Jenny,” obtaining a linear magnification of 2.5 when the stamp is held 2.76 cm from the lens. What is the focal length of the magnifying glass?
Solution:
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Chapter 27 Optical Instruments Q.92GP
IP A person needs glasses with a refractive power of –1.35 diopters to be able to focus on distant objects. (a) Is this person nearsighted or farsighted? Explain. (b) What is this person’s (unaided) far point?
Solution:
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Chapter 27 Optical Instruments Q.93GP
IP BIO A Big Eye The largest eye ever to exist on Earth belonged to an extinct species of ichthyosaur, Temnodontosaurus platyodon. This creature had an eye that was 26.4 cm in diameter. It is estimated that this ichthyosaur also had a relatively large pupil, giving it an effective aperture setting of about f/1.1. (a) Assuming its pupil was one-third the diameter of the eye, what was the approximate focal length of the ichthyosaur’s eye? (b) When the ichthyosaur narrowed its pupil in bright light, did its f-number increase or decrease? Explain.
Solution:
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Chapter 27 Optical Instruments Q.94GP
Consider a Galilean telescope, as illustrated in Figure 27–23, constructed from two lenses with focal lengths of 75.6 cm and –18.0 mm. (a) What is the distance between these lenses if an infinitely distant object is to produce an infinitely distant image? (b) What is the angular magnification when the lenses are separated by the distance calculated in part (a)?
Solution:
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Chapter 27 Optical Instruments Q.95GP
A converging lens forms a virtual object 12 cm to the right of a second lens that has a refracting power of 3.75 diopter. (a) Where is the image? (b) Is the image real or virtual? Explain.
Solution:
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Chapter 27 Optical Instruments Q.96GP
A farsighted person uses glasses with a refractive power of 3.6 diopters. The glasses are worn 2.5 cm from his eyes. What is this person’s near point when not wearing glasses?
Solution:
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Chapter 27 Optical Instruments Q.97GP
Landing on an Aircraft Carrier The Long-Range Lineup System (LRLS) used to ensure safe landings on aircraft carriers consists of a series of Fresnel lenses of different colors. Each lens focuses light in a different, specific direction, and hence which light a pilot sees on approach determines whether the plane is above, below, or on the proper landing path. The basic idea behind a Fresnel lens, which has the same optical properties as an ordinary lens, is shown in Figure 27-24, along with a photo of the LRLS. Suppose an object (a lightbulb in this case) is 17.1 cm behind a Fresnel lens, and that the corresponding image is a distance di = d in front of the lens. If the object is moved to a distance of 12.0 cm behind the lens, the image distance doubles to di =2d. hi the LRLS, it is desired to have the image of the lightbulb at infinity. What object distance will give this result for this particular lens?
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Solution:
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Chapter 27 Optical Instruments Q.98GP
When using a telescope to photograph a faint astronomical object, you need to maximize the amount of light energy that falls on each square millimeterof the image on the film. For a given telescope and object, the total light that falls on the film is proportional to the length of the exposure, so a long exposure will reveal fainter objects than a short exposure. Show that for a given length of exposure, the brightness of the image is inversely proportional to the square of the f-number of the telescope system.
Solution:
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Chapter 27 Optical Instruments Q.99GP
A Cassegrain astronomical telescope uses two mirrors to form the image. Tire larger (concave) objective mirror has a focal length f1 = +50.0 cm. A small convex secondary mirror is mounted 43.0 cm in front of the primary. As shown in Figure 27-25, light is reflected from the secondary through a hole in the center of the primary, thereby forming a real image 8.00 cm behind the primary mirror. What is the radius of curvature of the secondary mirror?
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Solution:
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Chapter 27 Optical Instruments Q.100GP
IP A convex lens (f = 20.0 cm) is placed 10.0 cm in front of a plane mirror. A matchstick is placed 25.0 cm in front of the lens, as shown in Figure 27-26. (a) If you look through the lens toward the mirror, where will you see the image of the matchstick? (b) Is the image real or virtual? Explain. (c) What is the magnification of the image? (d) Is the image upright or inverted?
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Solution:
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Chapter 27 Optical Instruments Q.101GP
Repeat Problem 100 for the case where the converging lens is replaced with a diverging lens with ƒ = –20.0 cm. Everything else in the problem remains the same.
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Solution:
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Chapter 27 Optical Instruments Q.102GP
· · · Repeat Problem 47 for the case where lens 1 is replaced with a diverging lens with f1 = –20.0 cm. Everything else in the problem remains the same.
Solution:
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Chapter 27 Optical Instruments Q.103GP
· · · The diameter of a collimated laser beam can be expanded or reduced by using two converging lenses, with focal lengths f1 and f2, mounted a distance f1 + f2 from each other, as shown in Figure 27-27. What is the ratio of the two beam diameters, (d1/d2), expressed in terms of the focal lengths?
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Solution:
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Chapter 27 Optical Instruments Q.104GP
Consider three lenses with focal lengths of 25.0 cm, –15.0 cm, and 11.0 cm positioned on the x axis at x = 0,x = 0.400 m, and x = 0.500 m, respectively. An object is at x = –122 cm. Find (a) the location and (b) the orientation and magnification of the final image produced by this lens system.
Solution:
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Chapter 27 Optical Instruments Q.105GP
· · · Because a concave lens cannot form a real image of a real object, it is difficult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the concave lens. Under the proper conditions, the concave lens will form a real image of the virtual object! A student conducting a laboratory project on concave lenses makes the following observations: When a lamp is placed 42.0 cm to the left of a particular convex lens, a real (inverted) image is formed 37.5 cm to the right of the lens. The lamp and convex lens are kept in place while a concave lens is mounted 15.0 cm to the right of the convex lens. A real image of the lamp is now formed 35.0 cm to the right of the concave lens. What is the focal length of each lens?
Solution:
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Chapter 27 Optical Instruments Q.106GP
· · · A person with a near-point distance N uses a magnifying glass with a focal length f. Show that the greatest magnification that can be achieved with this magnifier is M = 1 + N/f.
Solution:
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Chapter 27 Optical Instruments Q.107PP
A patient receives a rigid IOL whose focus cannot be changed—it is designed to provide clear vision of objects at infinity. The patient will use corrective contacts to allow for close vision. Should the refractive power of the corrective contacts be positive or negative?
Solution:
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Chapter 27 Optical Instruments Q.108PP
Referring to the previous problem, find the refractive powerof contacts that will allow the patient to focus on a book at adistance of 23.0 cm.
A. 0.0435 diopter
B. 0.230 diopter
C. 4.35 diopters
D. 8.70 diopters
Solution:
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Chapter 27 Optical Instruments Q.109PP
Suppose a flexible, adaptive IOL has a focal length of 3.00 cm.How far forward must the IOL move to change the focus ofthe eye from an object at infinity to an object at a distance of50.0 cm?
A. 1.9 mm
B. 2.8 mm
C. 3.1 mm
D. 3.2 mm
Solution:
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Chapter 27 Optical Instruments Q.110IP
IP Referring to Example 27–2 Suppose a person’s eyeglasses have a focaL length of −301 cm, are 2.00 cm in front of the eyes, and allow the person to focus on distant objects. (a) Is this person’s far point greater than or less than 323 cm, which is the far point for glasses the same distance from the eyes and with a focal length of −321 cm? Explain. (b) Find the far point for this person.
Solution:
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Chapter 27 Optical Instruments Q.111IP
IP Referring to Example 27–2 hi Example 27–2, a person has a far-point distance of 323 cm. If this person wears glasses 2.00 cm in front of the eyes with a focal length of −321 cm, distant objects can be brought into focus. Suppose a second person’s far point is 353 cm. (a) Is the magnitude of the focal length of the eyeglasses that allow this person to focus on distant objects greater than or less than 321 cm? Assume the glasses are 2.00 cm in front of the eyes. (b) Find the required focal length for the second person’s eyeglasses.
Solution:
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Chapter 27 Optical Instruments Q.112IP
IP Referring to Example 27–3 Suppose a person’s eyeglasses have a refractive power of 2.75 diopters and that they allow the person to focus on an object that is just 25.0 cm from the eye. The glasses are 2.00 cm in front of the eyes. (a) Is this person’s near point greater than or less than 57.0 cm, which is the near-point distance when the glasses have a refractive power of 2.53 diopters? Explain. (b) Find the near point for this person.
Solution:
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Chapter 27 Optical Instruments Q.113IP
IP Referring to Example 27–3 Suppose a person’s near-point distance is 67.0 cm. (a) Is the refractive power of the eyeglasses that allow this person to focus on an object just 25.0 cm from the eye greater than or less than 2.53 diopters, which is the refractive power when the near-point distance is 57.0 cm? The glasses are worn 2.00 cm in front of the eyes. (b) Find the required refractive power for this person’s eyeglasses.
Solution:
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