Download Section 1 A Particle Model of Waves: Practice Problems

Chapter 27 Practice Problems, Review, and Assessment
Section 1 A Particle Model of Waves: Practice Problems
Use E = 1240 eV·nm/λ to solve the following problems.
1. What is a photon’s energy if the photon’s wavelength is 515 nm?
SOLUTION: 2. A photon’s energy is 2.03 eV. What is the photon’s wavelength?
SOLUTION: 3. Rank the following photons from least to greatest energy.
A. 4.0 eV
B. 320 nm
C. 811 nm
D. 2.1 eV
SOLUTION: 4. CHALLENGE The diagram in Figure 6 shows the visible light spectrum. What is the range of energies associated
with photons in the visible light spectrum?
SOLUTION: Find the energy of violet and red light:
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Chapter 27 Practice Problems, Review, and Assessment
4. CHALLENGE The diagram in Figure 6 shows the visible light spectrum. What is the range of energies associated
with photons in the visible light spectrum?
SOLUTION: Find the energy of violet and red light:
The range of energies is 1.8 eV to 3.1 eV.
5. An electron has an energy of 2.3 eV. What is the kinetic energy of the electron in joules?
SOLUTION: 6. What is the velocity of the electron in the previous problem?
SOLUTION: 6 7. What is the kinetic energy in eV of an electron with a velocity of 6.2×10 m/s?
SOLUTION: 8. The stopping potential for a photoelectric cell is 5.7 V. Calculate the maximum kinetic energy of the emitted photoelectrons in eV.
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SOLUTION: Page 2
Chapter 27 Practice Problems, Review, and Assessment
8. The stopping potential for a photoelectric cell is 5.7 V. Calculate the maximum kinetic energy of the emitted photoelectrons in eV.
SOLUTION: 9. The stopping potential for a photoelectric cell is 5.1 V. How much kinetic energy does the incident light give the electrons in joules?
SOLUTION: 10. The maximum kinetic energy of emitted photoelectrons in a photoelectric cell is 7.5×10
potential?
–19 J. What is the stopping
SOLUTION: 11. CHALLENGE The stopping potential required to prevent current through a photocell is 3.2 V. Calculate the maximum kinetic energy in joules of the photoelectrons as they are emitted.
SOLUTION: 12. The threshold wavelength of zinc is 310 nm. Find the threshold frequency, in Hz, and the work function, in eV, of
zinc.
SOLUTION: 13. The work function for cesium is 1.95 eV. What is the maximum kinetic energy, in eV, of photoelectrons ejected eSolutions
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when 425-nm violet light falls on the cesium?
SOLUTION: Chapter 27 Practice Problems, Review, and Assessment
13. The work function for cesium is 1.95 eV. What is the maximum kinetic energy, in eV, of photoelectrons ejected when 425-nm violet light falls on the cesium?
SOLUTION: 14. When a metal is illuminated with 193-nm ultraviolet radiation, electrons with energies of 3.5 eV are emitted. What is the work function of the metal?
SOLUTION: 15. CHALLENGE A researcher illuminates a sample of metal and finds the longest wavelength to eject electrons is
273 nm. Use Table 1 to identify the most likely metal.
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Section 1 A Particle Model of Waves: Review
16. MAIN IDEA Why is high-intensity, low-frequency light unable to eject electrons from a metal, whereas lowintensity, high-frequency light can?
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Chapter 27 Practice Problems, Review, and Assessment
15. CHALLENGE A researcher illuminates a sample of metal and finds the longest wavelength to eject electrons is
273 nm. Use Table 1 to identify the most likely metal.
SOLUTION: Section 1 A Particle Model of Waves: Review
16. MAIN IDEA Why is high-intensity, low-frequency light unable to eject electrons from a metal, whereas lowintensity, high-frequency light can?
SOLUTION: Light, a form of electromagnetic radiation, is quantized and massless, yet it does have kinetic energy.
Each incident photon interacts with a single electron. If the incident photon does not have sufficient
energy, it cannot eject an electron. Because energy is directly related to frequency, low frequency light
does not have sufficient energy to eject an electron, whereas high frequency light does.
17. Frequency and Energy of Hot-Object Radiation As the temperature of an object is increased, how does the
frequency of peak intensity change? How does the total amount of radiated energy from the object change?
SOLUTION: Both frequency of peak intensity and total energy radiated increase. The peak frequency increases as T,
4
whereas the total energy increases as T .
18. Photoelectric and Compton Effects Distinguish the photoelectric effect from the Compton effect.
SOLUTION: The Compton effect is the scattering of a photon by matter, resulting in a photon of lower energy and
momentum. The photoelectric effect is the emission of electrons from a metal sample when radiation of
sufficient energy is incident on it.
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and by
Compton
19. Photoelectric
Effects An experimenter sends an X-ray into a target. An electron, but no other Page 5
radiation, emerges from the target. Explain whether this event is a result of the photoelectric effect or the Compton
effect.
SOLUTION: The Compton effect is the scattering of a photon by matter, resulting in a photon of lower energy and
Chapter
27 Practice
Review,
Assessment
momentum.
The Problems,
photoelectric
effectand
is the
emission of electrons from a metal sample when radiation of
sufficient energy is incident on it.
19. Photoelectric and Compton Effects An experimenter sends an X-ray into a target. An electron, but no other
radiation, emerges from the target. Explain whether this event is a result of the photoelectric effect or the Compton
effect.
SOLUTION: It is a result of the photoelectric effect, which is the capture of a photon by an electron in matter and the
transfer of the photon’s energy to the electron.
20. Photoelectric Effect Green light (λ = 532 nm) strikes an unknown metal, causing electrons to be ejected. The ejected electrons can be stopped by a potential of 1.44 V. What is the work function, in eV, of the metal?
SOLUTION: 21. Energy of a Photon What is the energy, in eV, of the photons produced by a laser pointer having a 650-nm
wavelength?
SOLUTION: 22. Compton Effect An X-ray strikes a bone, collides with an electron, and scatters. How does the wavelength of the
scattered X-ray compare to the wavelength of the incident X-ray?
SOLUTION: The scattered X-ray has a longer wavelength than the incoming X-ray.
23. Photoelectric Effect An X-ray is absorbed in a bone and releases an electron. If the X-ray has a wavelength of
approximately 0.02 nm, estimate the energy, in eV, of the electron. Assume that the work function of the bone is negligible compared to the X-ray’s energy.
SOLUTION: 24. Critical Thinking Imagine that the collision of two billiard balls models the interaction of a photon and an electron
during the Compton effect. Suppose the electron is replaced by a much more massive proton. Would this proton gain
as much energy from the collision as the electron does? Would the photon lose as much energy as it does when it
collides with the electron?
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The answer to both questions is no. Section 2 Matter Waves: Practice Problems
Page 6
negligible compared to the X-ray’s energy.
SOLUTION: Chapter 27 Practice Problems, Review, and Assessment
24. Critical Thinking Imagine that the collision of two billiard balls models the interaction of a photon and an electron
during the Compton effect. Suppose the electron is replaced by a much more massive proton. Would this proton gain
as much energy from the collision as the electron does? Would the photon lose as much energy as it does when it
collides with the electron?
SOLUTION: The answer to both questions is no. Section 2 Matter Waves: Practice Problems
25. What is the de Broglie wavelength and speed of an electron accelerated by a potential difference of 250 V?
SOLUTION: 26. A 7.0-kg bowling ball rolls with a velocity of 8.5 m/s.
a. What is the de Broglie wavelength of the bowling ball?
b. Why does the bowling ball exhibit no observable wave behavior?
SOLUTION: a.
\
b. The wavelength is too small to show observable effects.
27. What potential difference is needed to accelerate an electron so it has a 0.125-nm wavelength?
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\
Chapter
27 Practice Problems, Review, and Assessment
b. The wavelength is too small to show observable effects.
27. What potential difference is needed to accelerate an electron so it has a 0.125-nm wavelength?
SOLUTION: 28. CHALLENGE The electron in Example Problem 3 has a de Broglie wavelength of 0.14 nm. What is the kinetic energy, in eV, of a proton with the same wavelength?
SOLUTION: Section 2 Matter Waves: Review
29. MAIN IDEA De Broglie’s theory of matter waves provides a way to calculate the wavelength of any moving
particle. Explain why the wave nature of everyday objects is not obvious.
SOLUTION: The wavelengths of most objects are much too small to be detected.
30. De Broglie Wavelength An alpha particle (helium nucleus) has a mass of 6.6×10
of 120 m/s. What is this alpha particle’s de Broglie wavelength?
–27 kg and is moving at a speed
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29. MAIN IDEA De Broglie’s theory of matter waves provides a way to calculate the wavelength of any moving
particle. Explain why the wave nature of everyday objects is not obvious.
SOLUTION: Chapter
27 Practice Problems,
Review,
Assessment
The wavelengths
of most objects
areand
much
too small to be detected.
30. De Broglie Wavelength An alpha particle (helium nucleus) has a mass of 6.6×10
of 120 m/s. What is this alpha particle’s de Broglie wavelength?
–27 kg and is moving at a speed
SOLUTION: 31. De Broglie Wavelength What is the de Broglie wavelength of an electron accelerated through a potential
difference of 125 V?
SOLUTION: 32. Critical Thinking When light or a beam of atoms passes through a double slit, an interference pattern forms even
when photons or atoms pass through the slits one at a time. How does the Heisenberg uncertainty principle explain
this?
SOLUTION: The Heisenberg uncertainty principle states that you cannot simultaneously know the precise position
and momentum of a particle. Thus, if you know the precise position of a photon or an atom as it passes
through the slit, you cannot know its precise momentum. In practice, any experiment you do to measure
the position of the photon or the atom as it passes through one slit or the other changes the momentum
of the atom or the photon such that the interference pattern is destroyed. Chapter Assessment Section 1 A Particle Model of Waves: Mastering Concepts
33. Incandescent Light An incandescent lightbulb is controlled by a dimmer. What happens to the color of the light
given off by the bulb as the potential difference applied to the bulb decreases?
SOLUTION: The light becomes redder.
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34. Describe the concept of quantized energy.
SOLUTION: Page 9
The Heisenberg uncertainty principle states that you cannot simultaneously know the precise position
and momentum of a particle. Thus, if you know the precise position of a photon or an atom as it passes
through the slit, you cannot know its precise momentum. In practice, any experiment you do to measure
Chapter
27 Practice
Problems,
and
the position
of the
photon orReview,
the atom
asAssessment
it passes through one slit or the other changes the momentum
of the atom or the photon such that the interference pattern is destroyed. Chapter Assessment Section 1 A Particle Model of Waves: Mastering Concepts
33. Incandescent Light An incandescent lightbulb is controlled by a dimmer. What happens to the color of the light
given off by the bulb as the potential difference applied to the bulb decreases?
SOLUTION: The light becomes redder.
34. Describe the concept of quantized energy.
SOLUTION: Quantized energy means that energy can exist only in whole number multiples of some minimum value.
35. What quantity is quantized in Max Planck’s interpretation of the radiation emitted by objects?
SOLUTION: The vibrational energy of the incandescent atoms is quantized.
36. BIG IDEA What is a quantum of light called?
SOLUTION: a photon
37. Light above the threshold frequency shines on the metal cathode in a photocell. How does Einstein’s photoelectric
effect theory explain the fact that as the light intensity increases, photoelectron current increases?
SOLUTION: Each photon ejects a photoelectron. Light with greater intensity contains more photons per second; thus,
it causes the ejection of more photo electrons per second.
38. Describe how Einstein’s photon theory accounts for the fact that light below the threshold frequency of a metal
produces no photoelectrons, regardless of the intensity of the light.
SOLUTION: Photons below the threshold frequency do not have sufficient energy to eject an electron. If the intensity
of the light increases, the number of photons increases but their energy does not; the photons are still
unable to eject an electron.
39. Photographic Film Older cameras recorded images on film. Because certain types of black-and-white film were
not sensitive to red light, they could be developed in a darkroom illuminated by red light. How does the photon model
of light explain this?
SOLUTION: Red photons do not have enough energy to cause the chemical reaction that exposes film.
40. How does the Compton effect demonstrate that photons have momentum as well as energy?
SOLUTION: Elastic collisions transfer both momentum and energy. Only if photons have momentum can the
equations be satisfied.
Chapter Assessment
Section 1 A Particle Model of Waves: Mastering Problems
41. According to Planck’s theory, what is the frequency of vibration of an atom if it gives off 5.44×10
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changing its value of n by 1? (Level 1)
SOLUTION: −19 J while
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40. How does the Compton effect demonstrate that photons have momentum as well as energy?
SOLUTION: Chapter
27 collisions
Practice Problems,
Review,
and Assessment
Elastic
transfer both
momentum
and energy. Only if photons have momentum can the
equations be satisfied.
Chapter Assessment
Section 1 A Particle Model of Waves: Mastering Problems
41. According to Planck’s theory, what is the frequency of vibration of an atom if it gives off 5.44×10
changing its value of n by 1? (Level 1)
−19 J while
SOLUTION: 42. What potential difference is needed to stop electrons with a maximum kinetic energy of 4.8×10
−19 J? (Level 1)
SOLUTION: 2 43. What is the momentum of a photon of violet light that has a wavelength of 4.0×10 nm? (Level 1)
SOLUTION: 14 44. The threshold frequency of a certain metal is 3.00×10 Hz. What is the maximum kinetic energy of an ejected
2 photoelectron if the metal is illuminated by light with a wavelength of 6.50×10 nm? (Level 2)
SOLUTION: 14 45. The threshold frequency of sodium is 4.4×10 Hz. How much work must be done to free an electron from the
surface of sodium? (Level 2)
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15 46. If light with a frequency of 1.00×10 Hz falls on the sodium in the previous problem, what is the maximum kinetic
energy of the photoelectrons? (Level 2)
Chapter 27 Practice Problems, Review, and Assessment
14 45. The threshold frequency of sodium is 4.4×10 Hz. How much work must be done to free an electron from the
surface of sodium? (Level 2)
SOLUTION: 15 46. If light with a frequency of 1.00×10 Hz falls on the sodium in the previous problem, what is the maximum kinetic
energy of the photoelectrons? (Level 2)
SOLUTION: 47. The stopping potential of a certain metal is shown in Figure 14. What is the maximum kinetic energy of the
photoelectrons in the following units? (Level 2)
a. electron volts
b. joules
SOLUTION: a. b. eSolutions Manual - Powered by Cognero
48. Light Meter A photographer’s light meter uses a photocell to measure the light falling on the subject to be
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Chapter 27 Practice Problems, Review, and Assessment
47. The stopping potential of a certain metal is shown in Figure 14. What is the maximum kinetic energy of the
photoelectrons in the following units? (Level 2)
a. electron volts
b. joules
SOLUTION: a. b. 48. Light Meter A photographer’s light meter uses a photocell to measure the light falling on the subject to be
photographed. What should be the work function of the cathode if the photocell is to be sensitive to red light
(λ = 680 nm) as well as to the other colors of light? (Level 3)
SOLUTION: 11 49. Solar Energy A home uses about 4×10 J of energy each year. In many parts of the United States, there are about
3000 h of sunlight each year. On average, each square meter of Earth’s surface receives about 1000 J of energy per
second (1000 W) from the Sun. (Level 3)
a. How much energy from the Sun falls on one square meter each year?
b. If this solar energy can be converted to useful energy with an efficiency of 20 percent, how large an area of converters would produce the energy needed by the home?
SOLUTION: a.
2
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Earth
receives
about
1000 J/m each second, so
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SOLUTION: Chapter 27 Practice Problems, Review, and Assessment
11 49. Solar Energy A home uses about 4×10 J of energy each year. In many parts of the United States, there are about
3000 h of sunlight each year. On average, each square meter of Earth’s surface receives about 1000 J of energy per
second (1000 W) from the Sun. (Level 3)
a. How much energy from the Sun falls on one square meter each year?
b. If this solar energy can be converted to useful energy with an efficiency of 20 percent, how large an area of converters would produce the energy needed by the home?
SOLUTION: a.
2
Earth receives about 1000 J/m each second, so
b.
Chapter Assessment
Section 2 Matter Waves: Mastering Concepts
50. The momentum, p , of a particle of matter is given by p = mv. Can you calculate the momentum of a photon using the
same equation? Explain.
SOLUTION: No, using the equation yields a photon momentum of zero because photons are massless. This result is
incorrect because massless photons have non zero momenta.
51. Describe a method for measuring each of the following electron properties.
a. charge
b. mass
c. wavelength
SOLUTION: a. Balance the force of gravity against the force of an electric field on the charge.
b. Balance the force of an electric field against that of a magnetic field to find m/q, then use the measured
value of q.
c. Scatter electrons off a crystal and measure the angles of diffraction.
52. Describe how each of the following photon properties could be measured. a. energy
b. momentum
c. wavelength
SOLUTION: a. Measure the KE of the electrons ejected from a metal for at least two different wavelengths, or
measure
KE ofbythe
electrons ejected from a known metal at only one wavelength.
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b. Measure the change in wavelength of X-rays scattered by matter.
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SOLUTION: a. Balance the force of gravity against the force of an electric field on the charge.
b. Balance the force of an electric field against that of a magnetic field to find m/q, then use the measured
value27
ofPractice
q.
Chapter
Problems, Review, and Assessment
c. Scatter electrons off a crystal and measure the angles of diffraction.
52. Describe how each of the following photon properties could be measured. a. energy
b. momentum
c. wavelength
SOLUTION: a. Measure the KE of the electrons ejected from a metal for at least two different wavelengths, or
measure the KE of the electrons ejected from a known metal at only one wavelength.
b. Measure the change in wavelength of X-rays scattered by matter.
c. Measure the angle of diffraction when light passes through two slits or a diffraction grating, measure
the width of a single-slit diffraction pattern, or measure the angle the light is bent when it passes through
a prism.
Chapter Assessment
Section 2 Matter Waves: Mastering Problems
6 53. What is the de Broglie wavelength of an electron moving at 3.0×10 m/s? (Level 1)
SOLUTION: −10 54. What velocity would an electron need to have a de Broglie wavelength of 3.0×10
m? (Level 1)
SOLUTION: 3 55. A cathode-ray tube accelerates an electron from rest across a potential difference of 5.0×10 V. (Level 2)
a. What is the velocity of the electron?
b. What is the electron’s wavelength?
SOLUTION: a.
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Chapter 27 Practice Problems, Review, and Assessment
3 55. A cathode-ray tube accelerates an electron from rest across a potential difference of 5.0×10 V. (Level 2)
a. What is the velocity of the electron?
b. What is the electron’s wavelength?
SOLUTION: a.
b. 56. The kinetic energy of a hydrogen atom’s electron is 13.65 eV. (Level 2)
a. Find the velocity of the electron.
b. Calculate the electron’s de Broglie wavelength.
c. Given that a hydrogen atom’s radius is 0.519 nm, calculate the circumference of a hydrogen atom and compare it with the de Broglie wavelength for the atom’s electron.
SOLUTION: a. b. eSolutions Manual - Powered by Cognero
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27 Practice Problems, Review, and Assessment
Chapter
56. The kinetic energy of a hydrogen atom’s electron is 13.65 eV. (Level 2)
a. Find the velocity of the electron.
b. Calculate the electron’s de Broglie wavelength.
c. Given that a hydrogen atom’s radius is 0.519 nm, calculate the circumference of a hydrogen atom and compare it with the de Broglie wavelength for the atom’s electron.
SOLUTION: a. b. c. 57. Ranking Task Rank the following particles according to their de Broglie wavelength, from greatest to least.
Specifically indicate any ties. (Level 2)
A. an electron with a speed of 300 m/s
B. an electron with a speed of 500 m/s
C. a proton with a speed of 3 m/s
D. a proton with a speed of 500 m/s
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Chapter
27 Practice Problems, Review, and Assessment
57. Ranking Task Rank the following particles according to their de Broglie wavelength, from greatest to least.
Specifically indicate any ties. (Level 2)
A. an electron with a speed of 300 m/s
B. an electron with a speed of 500 m/s
C. a proton with a speed of 3 m/s
D. a proton with a speed of 500 m/s
SOLUTION: 58. An electron has a de Broglie wavelength of 0.18 nm. (Level 3)
a. How large a potential difference did it experience if it started from rest?
b. If a proton has a de Broglie wavelength of 0.18 nm, how large is the potential difference that it experienced if it started from rest?
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Chapter
27 Practice Problems, Review, and Assessment
58. An electron has a de Broglie wavelength of 0.18 nm. (Level 3)
a. How large a potential difference did it experience if it started from rest?
b. If a proton has a de Broglie wavelength of 0.18 nm, how large is the potential difference that it experienced if it started from rest?
SOLUTION: a. b. Chapter Assessment: Applying Concepts
59. Two iron bars are held in a fire. One glows dark red, while the other glows bright orange.
a. Which bar is hotter?
b. Which bar is radiating more energy?
SOLUTION: a. the rod glowing bright orange
b. the rod glowing bright orange
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Chapter 27 Practice Problems, Review, and Assessment
Chapter Assessment: Applying Concepts
59. Two iron bars are held in a fire. One glows dark red, while the other glows bright orange.
a. Which bar is hotter?
b. Which bar is radiating more energy?
SOLUTION: a. the rod glowing bright orange
b. the rod glowing bright orange
60. Will high-frequency light eject a greater number of electrons from a photosensitive surface than low-frequency light,
assuming that both frequencies are above the threshold frequency?
SOLUTION: Not necessarily; the number of ejected electrons is proportional to the number of incident photons or the
brightness of the light, not the frequency of the light.
61. Potassium can emit photoelectrons when struck by blue light, whereas tungsten requires ultraviolet radiation in order
to emit photoelectrons.
a. Which metal has a higher threshold frequency?
b. Which metal has a larger work function?
SOLUTION: a. Blue light has a lower frequency and energy than UV light. Thus, tungsten has the higher threshold
frequency.
b. tungsten
62. Compare the de Broglie wavelength of the baseball shown in Figure 15 with the diameter of the baseball.
SOLUTION: −34
The diameter of the baseball is about 0.10 m, whereas the de Broglie wavelength is 10
is about 1033 times larger than the wavelength.
m; the baseball
Chapter Assessment: Mixed Review
63. What is the maximum kinetic energy of photoelectrons ejected from a metal that has a stopping potential of 3.8 V? (Level 1)
SOLUTION: KE = –eV0
= –(–1 elementary charge)(3.8 V)
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= 3.8 eV
64. The threshold frequency of a certain metal is 8.0×10
Page 20
14 Hz. What is the metal’s work function? (Level 1)
SOLUTION: −34
The diameter
of Problems,
the baseball
is about
0.10
m, whereas the de Broglie wavelength is 10
Chapter
27 Practice
Review,
and
Assessment
33
is about 10 times larger than the wavelength.
m; the baseball
Chapter Assessment: Mixed Review
63. What is the maximum kinetic energy of photoelectrons ejected from a metal that has a stopping potential of 3.8 V? (Level 1)
SOLUTION: KE = –eV0
= –(–1 elementary charge)(3.8 V)
= 3.8 eV
64. The threshold frequency of a certain metal is 8.0×10
14 Hz. What is the metal’s work function? (Level 1)
SOLUTION: W = hf 0
= (6.63×10–34 J/Hz)(8.0×1014 Hz)
–19
= 5.3×10
J
15 65. If light with a frequency of 1.6×10 Hz falls on the metal in the previous problem, what is the maximum kinetic
energy of the photoelectrons? (Level 1)
SOLUTION: KE = h f – h f 0
= (6.63×10–34 J/Hz)(1.6×1015 Hz) – 5.3×10-19 J
= 5.3×10
–19
J
2
−27 66. Find the de Broglie wavelength of a deuteron (nucleus of H isotope) of mass 3.3×10
kg that moves with a speed
4 of 2.5×10 m/s. (Level 1)
SOLUTION: 67. The work function for a certain piece of iron is 4.7 eV. (Level 2) a. What is the threshold wavelength of iron?
b. Iron is exposed to radiation of wavelength 150 nm. What is the maximum kinetic energy of the ejected electrons in
eV?
SOLUTION: a. eSolutions Manual - Powered by Cognero
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Chapter 27 Practice Problems, Review, and Assessment
67. The work function for a certain piece of iron is 4.7 eV. (Level 2) a. What is the threshold wavelength of iron?
b. Iron is exposed to radiation of wavelength 150 nm. What is the maximum kinetic energy of the ejected electrons in
eV?
SOLUTION: a. b. 68. Barium has a work function of 2.48 eV. What is the longest wavelength of light that will cause electrons to be emitted from barium? (Level 2)
SOLUTION: 69. An electron has a de Broglie wavelength of 400.0 nm, the shortest wavelength of visible light. (Level 2)
a. Find the velocity of the electron.
b. Calculate the energy of the electron in eV.
SOLUTION: a.
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b.
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Chapter 27 Practice Problems, Review, and Assessment
69. An electron has a de Broglie wavelength of 400.0 nm, the shortest wavelength of visible light. (Level 2)
a. Find the velocity of the electron.
b. Calculate the energy of the electron in eV.
SOLUTION: a.
b.
15 70. Incident radiation falls on tin, as shown in Figure 16. The threshold frequency of tin is 1.2×10 Hz. (Level 3)
a. What is the threshold wavelength of tin?
b. What is the work function of tin?
c. The incident electromagnetic radiation has the wavelength indicated in Figure 16. What is the kinetic energy of
the ejected electrons in eV?
SOLUTION: a. eSolutions Manual - Powered by Cognero
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Chapter 27 Practice Problems, Review, and Assessment
15 70. Incident radiation falls on tin, as shown in Figure 16. The threshold frequency of tin is 1.2×10 Hz. (Level 3)
a. What is the threshold wavelength of tin?
b. What is the work function of tin?
c. The incident electromagnetic radiation has the wavelength indicated in Figure 16. What is the kinetic energy of
the ejected electrons in eV?
SOLUTION: a. b.
c.
Chapter Assessment: Thinking Critically
71. Apply Concepts Just barely visible light with an intensity of 1.5×10
Figure 17.
–11 2
W/m enters a person’s eye, as shown in
a. If this light shines into the person’s eye and passes through the person’s pupil, what is the power, in watts, that
enters the person’s eye?
b. Use
the given
wavelength
of 24
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photons per second entering the eye.
Chapter 27 Practice Problems, Review, and Assessment
Chapter Assessment: Thinking Critically
71. Apply Concepts Just barely visible light with an intensity of 1.5×10
Figure 17.
–11 2
W/m enters a person’s eye, as shown in
a. If this light shines into the person’s eye and passes through the person’s pupil, what is the power, in watts, that
enters the person’s eye?
b. Use the given wavelength of the incident light and information provided in Figure 17 to calculate the number of
photons per second entering the eye.
SOLUTION: a. Power = (intensity)(area)
= (intensity)(πr2)
–11
2
–11
= (1.5×10 W/m )(π(3.5×10
= 5.8×10–16 W
b. Energy per photon
2
m) )
72. Problem Posing Complete this problem so that it must be solved using the work function: “Light of wavelength
443 nm is incident upon an unknown metal…”
SOLUTION: A possible form of the correct answer would be, “ and ejects electrons with a kinetic energy of 1.56 eV.
What is the metal’s work function?”
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A student
73. Make
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completed a photoelectric-effect experiment and recorded the stopping potential
as a function of wavelength, as shown in Table 2. The photocell had a sodium cathode. Plot the stopping potential
versus frequency. Use your calculator to draw the best-fit straight line (regression line). From the slope and intercept
443 nm is incident upon an unknown metal…”
SOLUTION: Chapter
27 Practice
Problems,
Review,
and
Assessment
A possible
form of
the correct
answer
would
be, “ and ejects electrons with a kinetic energy of 1.56 eV.
What is the metal’s work function?”
73. Make and Use Graphs A student completed a photoelectric-effect experiment and recorded the stopping potential
as a function of wavelength, as shown in Table 2. The photocell had a sodium cathode. Plot the stopping potential
versus frequency. Use your calculator to draw the best-fit straight line (regression line). From the slope and intercept
of the line, find the work function, the threshold wavelength, and the value of h/e from this experiment. Compare the
value of h/e to the accepted value.
SOLUTION: Convert wavelength to frequency and plot. Determine the best straight line through the data.
−15
−15
J/Hz•C
Slope = 4.18×10 V/Hz = 4.18×10
The accepted value is
From the graph, the threshold frequency is f 0 = 4.99×1014 Hz, which gives a threshold wavelength of and a work function of 74. Reverse Problem Write a physics problem with real objects for which the following equation would be part of the
solution:
SOLUTION: Answers will vary, but a correct form of the answer is, “A photon’s momentum is 1.19×10−27 kg•m. What
is the photon’s wavelength?”
Chapter Assessment: Writing in Physics
most massive
75. Research
eSolutions
Manualthe
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by Cogneroparticle
how the interference was created.
SOLUTION: for which interference effects have been seen. Describe the experiment and
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SOLUTION: Answers
will vary,
but a correct
formand
of the
answer is, “A photon’s momentum is 1.19×10−27 kg•m. What
Chapter
27 Practice
Problems,
Review,
Assessment
is the photon’s wavelength?”
Chapter Assessment: Writing in Physics
75. Research the most massive particle for which interference effects have been seen. Describe the experiment and
how the interference was created.
SOLUTION: This is an active field of research, but at the time of this text's publication the most massive particles
shown to exhibit interference effects are molecules consisting of up to 430 atoms. An international team
of physicists published results in 2011 describing an experiment in which a beam of these molecules,
which can be up to 6 nm in diameter, create an interference pattern when passed through a virtual
diffraction grating made of laser light. Chapter Assessment: Cumulative Review
76. The spring in a pogo stick is compressed 15 cm when a child who weighs 400.0 N stands on it. What is the spring constant of the spring?
SOLUTION: F = kx
77. A marching band sounds flat on a cold day. Why?
SOLUTION: The pitch of a wind instrument depends on the speed of sound in the air within it. The colder the air, the
lower the speed of sound and the flatter the pitch of the sound produced.
−7 78. A charge of 8.0×10 C experiences a force of 9.0 N when placed 0.02 m from a second charge. What is the magnitude of the second charge?
SOLUTION: 79. A homeowner buys a dozen identical 120-V light sets. Each light set has 24 bulbs connected in series, and the resistance of each bulb is 6.0 V. Calculate the total load in amperes if the homeowner operates all the sets from a single exterior outlet.
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Chapter 27 Practice Problems, Review, and Assessment
79. A homeowner buys a dozen identical 120-V light sets. Each light set has 24 bulbs connected in series, and the resistance of each bulb is 6.0 V. Calculate the total load in amperes if the homeowner operates all the sets from a single exterior outlet.
SOLUTION: 80. The force on a 1.2-m wire is 1.1×10
in the wire?
−3 N. The wire is perpendicular to Earth’s magnetic field. How much current is
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