1. Photons of wavelength λ are Compton scattered from electrons, and the scattered photons of wavelength λ′ are observed at an angle of 90 degrees relative to the direction of the incident photons.
(a) If the detector of the scattered photons is moved to an angle that is smaller than 90 degrees, the wavelength of the scattered photons will:
(1) increase (2) decrease (3) remain the same
(4) increase at some angles between 0 and 90 degrees and decrease at other angles (b) If the source of incident photons is replaced with one that produces photons of much larger wavelength, how does the change in wavelength Δλ = λ′ - λ measured at 90 degrees compare with that of the original source?
(1) Δλ increases (2) Δλ decreases (3) Δλ remains the same 2. Compton scattering suggests that the light scattered from objects should change
wavelength when the objects are viewed from different angles. Why don’t we observe objects changing color as we vary the viewing angle?
3. In a photoelectric experiment, changing one of the experimental conditions might produce one of the following results:
(1) Increase the photoelectric current. (2) Increase the stopping potential. (3) Decrease the photoelectric current. (4) Decrease the stopping potential. Choose the outcome that would occur after the following changes:
(a) Replace the light source with one of twice the frequency but emitting the same number of photons per second.
(b) Replace the light source with one of twice the wavelength but emitting the same number of photons per second.
(c) Replace the light source with one of the same frequency but emitting twice as many photons per second.
(d) Without changing the light source, replace the emitter surface with a material having a smaller work function.
4. Possible interactions between electrons and photons can be represented symbolically by the 5 processes listed below. For each process, give the conventional name for the process, state whether it can occur for isolated particles, and describe how energy is conserved in the process.
(a) photon → electron + positron (b) electron + positron → photons
(c) electron → electron + photon (d) photon + electron → photon + electron (e) photon + electron → electron
Answers 1. (a) 2 (b) 3 2. Δ ∼λ 0.001 nm 3. (a) 2 (b) 4 (c) 1 (d) 2
Sample Exam Questions A. Multiple Choice
1. Some stars appear to have a color that is more blue than the color of the Sun. How would the surface temperature of a blue star compare with the surface temperature of the Sun?
(a) Tblue star > TSun (b) Tblue star < TSun
2. The most intense radiation emitted from a hot sample of metal has a wavelength of 60 μm. When the temperature of the sample is doubled, what will be the wavelength of the most intense radiation?
(a) 30 μm (b) 120 μm (c) 960 μm (d) 15 μm 3. A glowing object emits radiation with a spectrum in which there is one particular
wavelength at which the maximum intensity occurs. If the temperature of the object is doubled, what happens to the wavelength of the intensity maximum?
(a) Remains the same (b) Becomes twice as large (c) Becomes half as large (d) Becomes 4 times as large (e) Becomes 16 times as large
4. The Sun’s yellow color corresponds to a surface temperature of about 5500 K. What would be the color of a star with surface temperature of 7000 K?
(a) red (longer wavelength) (b) blue (shorter wavelength) (c) yellow (same wavelength)
5. Electrons are accelerated through a potential difference of 2000 volts and are incident on a metal surface, resulting in the emission of photons. Which of the following photon wavelengths would NOT be observed from this surface?
(a) 0.24 nm (b) 0.78 nm (c) 1.25 nm (d) 3.62 nm 6. Light of wavelength 477 nm is incident on the surfaces of several different metals.
For which value of the work function will electrons be emitted from the surface? (a) 4.2 eV (b) 3.7 eV (c) 3.2 eV (d) 2.3 eV
7. When photons of wavelength 488 nm are incident on a metal surface, electrons of maximum kinetic energy 1.39 eV are emitted from the surface. What is the minimum energy needed to remove an electron from this metal?
(a) 2.54 eV (b) 3.93 eV (c) 0.65 eV (d) 1.15 ev
8. For a certain metal surface, electrons are emitted when the surface is illuminated with light of wavelength below 435 nm but for no wavelengths above 435 nm. What is the work function of this surface?
(a) 1.36 eV (b) 2.85 eV (c) 3.48 eV (d) None of these values.
9. At temperature T a body emits its most intense radiation at a wavelength of 5.6 μm. What is the wavelength of the most intense radiation emitted by the same body at temperature 4T?
(a) 22.4 μm (b) 4.0 μm (c) 1.4 μm (d) 7.8 μm (e) 5.6 μm
10. Electrons of maximum kinetic energy K1 are released when X rays of wavelength λ1 are incident on the surface of a metal. If the light source is replaced by another that emits photons at the same rate but of longer wavelength λ2, how is the resulting maximum kinetic energy K2 related to K1?
(a) K2 = K1 (b) K2 > K1 (c) K2 < K1
11. Electrons are emitted when an ultraviolet light source of wavelength λ illuminates a certain metal surface. If you wanted to increase the number of electrons per unit time emitted from the surface, you should
(a) increase the frequency of the light source (b) increase the wavelength of the light source
(c) add a second light source identical to the first light source
12. A metal surface is illuminated with light of wavelength λ, and a resulting current i is observed in an electric circuit connected to the surface. The source is replaced with a different one in which the photon emission rate is only half as large. What should be the wavelength of this second source in order that the current have the same value i? (a) 2λ (b) λ/2 (c) > 2λ (d) < λ/2
(e) The experiment is impossible -- the second source can never give the same current i.
13. Which one of these processes involves a decrease in the kinetic energy of an electron? (a) bremsstrahlung (b) photoelectric effect (c) Compton scattering (d) pair production
Answers 1. a 2. a 3. c 4. b 5. a 6. d 7. d 8. b 9. c 10. c 11. c 12. e 13. a
B. Conceptual
1. Photons of wavelength λ are incident on a metal target. Scattered photons are observed at an angle θ1 relative to the direction of the original photons. In this geometry, it is determined that the scattered electrons have kinetic energy K1. If the scattered photons were observed at a larger angle, would the corresponding kinetic energy of the scattered electrons be greater than K1, equal to K1, or less than K1? EXPLAIN YOUR ANSWER.
2. A beam of photons of energy E is incident on a metal target. The photons scatter from the nearly free electrons in the target, and the scattered photons are observed at an angle θ relative to the direction of the original beam of photons. When the
photons emerge at that angle, the scattered electrons have a certain kinetic energy. As the angle θ is made smaller, does the corresponding kinetic energy of the scattered electrons increase, decrease, or remain the same? EXPLAIN YOUR ANSWER. 3. Consider two monochromatic (single-wavelength) light sources emitting light of
respective wavelengths λ1 and λ2, with λ2 > λ1. The two bulbs are otherwise identical and emit light with exactly the same intensity (in W/m2). A detector placed a distance d from bulb 1 (emitting at wavelength λ1) records N photons per second. When the same detector is placed at the same distance d from bulb 2 (emitting at wavelength
λ2), is the number of photons per second recorded by the detector greater than N, smaller than N, or equal to N? EXPLAIN YOUR ANSWER.
4. A source of light of wavelength λ is incident on a metal surface, and electrons of maximum kinetic energy K are observed to be emitted from the surface. The source is replaced by a different source that emits the same power (in watts) but has a smaller wavelength. Does the rate at which electrons are emitted from the surface increase, decrease, or remain the same, and does their maximum kinetic energy increase, decrease, or remain the same? EXPLAIN YOUR ANSWERS.
5. A beam of photons of energy E1 strikes a metal surface, and electrons are observed to be emitted at a rate that produces a current i1 in an external circuit. If the photon energy is increased while the number of photons per second striking the surface is kept constant, does the current in the external circuit increase, decrease, or remain the same? EXPLAIN YOUR ANSWER.
6. When a certain light source illuminates a metal surface, electrons are emitted from the metal with kinetic energies up to the value K. The light source is replaced with one that has the same wavelength but less intensity. With this new light source, does the upper limit of the electron kinetic energies increase, decrease, or remain the same? EXPLAIN YOUR ANSWER.
7. Consider an experiment in which a beam of monoenergetic photons is incident on free electrons. The scattered electrons are observed with an energy E1 when the scattered photons are observed at an angle θ1. For the same incident photons, when the scattered photons are observed at an angle that is smaller than θ1 do the scattered electrons have an energy that is greater than E1, less than E1, or equal to E1? EXPLAIN YOUR ANSWER.
8. The walls of a hollow metal box are maintained at a temperature T = 1000 K. The box is filled with photons in equilibrium with the walls. A tiny hole in one of the walls allows a small number of the photons to escape. Your equipment measures the number of escaping photons in a small interval of wavelength dλ at a wavelength of 10-5 m. If you raise the temperature of the box to 2000 K, would you expect the number of photons in the same interval at the same wavelength to increase, decrease, or stay about the same? EXPLAIN YOUR ANSWER.
9. A beam of ultraviolet light is incident on a metal surface. Electrons leave the surface with a range of kinetic energies from very small values up to some maximum value. If the light source is replaced by a different source that emits photons at the same rate but with smaller wavelength, does the range of electron kinetic energies become larger, become smaller, or remain the same? EXPLAIN YOUR ANSWER. 10. In Einstein’s explanation of the photoelectric effect, for a fixed wavelength the
number of emitted photoelectrons is [directly proportional to, independent of] the intensity of the incident radiation and the kinetic energy of the emitted photoelectrons is [directly proportional to, independent of] the intensity of the incident radiation. EXPLAIN YOUR ANSWERS.
11. X rays of wavelength λ1 are incident on a material, and scattered X rays of
wavelength λ1 + Δλ1 are observed at the scattering angle θ. The source of X rays is now replaced with a source of wavelength λ2 which is greater than λ1, and at the same angle θ the scattered X rays now have wavelength λ2 + Δλ2. Is Δλ2 greater than, equal to, or less than Δλ1? EXPLAIN YOUR ANSWER.
12. The walls of a hollow metal box are maintained at a temperature T = 1000 K. The box is filled with photons in equilibrium with the walls. A tiny hole in one of the walls allows a small number of the photons to escape. Your equipment measures the number of escaping photons in a small interval of wavelength dλ at a wavelength of 10-5 m. If you raise the temperature of the box to 2000 K, would you expect the number of photons in the same interval at the same wavelength to increase, decrease, or stay about the same? EXPLAIN YOUR ANSWER.
Answers 1. greater than 2. decrease 3. greater than