Download Chapter 28

Quantum Physics
1. What is the relationship between the stopping potential for photoelectrons and the intensity of the
radiation striking the metal?
a. It is an inverse square relationship.
b. It is a linear relationship.
c. There is none. The two quantities are independent.
d. It is an inverse first power relationship.
e. It is a direct proportion with the proportionality between the first power and the square.
ANS: c
2. What is the minimum energy that binds an electron in a metal?
a. The stopping potential
b. The work function
c. A quantum oscillation
d. A thermal release
e. The cutoff frequency
ANS: b
3. A 15 kg mass, attached to a massless spring whose force constant is 2500 N/m, vibrates with an amplitude
of 4.0 cm. Assume the energy is quantized, so that En  nhf . Find the quantum number, n of the system.
( h  6.626  10 34 J s )
a. 1.5  10 33
b. 3.0  10 33
c. 4.5  10 33
d. 5.4  10 33
e. 1.0  10 33
ANS: a
4. An energy of 13.6 eV is needed to ionize an electron from the ground state of a hydrogen atom. What
wavelength in nm is needed if a photon accomplishes this task? ( h  6.626 10 34 J s; c  3.00 10 8 m / s)
a. 60
b. 80
c. 70
d. 90
e. 40
507
508
Quantum Physics
ANS: d
Chapter 28
509
5. The cutoff wavelength for photoelectric emission of a particular substance is 500 nm. What is the work
function in eV? ( h  6.626 10 34 J s; c  3.00 10 8 m / s)
a. 4.2
b. 4.0  10 19
c. 4.0  10 10
d. 2.5  10 19
e. 2.5
ANS: e
6. What is the maximum velocity in km/s of a photoelectron emitted from a surface whose work function is
5.0 eV when the surface is illuminated by radiation of 200 nm wavelength?
( h  6.626  10 34 J  s; c  3.00  10 8 m / s; e  1.60  10 19 C)
a. 460
b. 650
c. 420
d. 550
e. 1480
ANS: b
7. A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm. What is the cutoff
wavelength of this material in nm? ( h  6.626  10 34 J  s; c  3.00  10 8 m / s; e  1.60  10 19 C)
a. 300
b. 200
c. 400
d. 100
e. 600
ANS: c
8. A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm. The work function in eV
of the material is ( h  6.626  10 34 J  s; c  3.00  10 8 m / s; e  1.60  10 19 C)
a. 4
b. 3
c. 5
d. 6
e. 2
ANS: b
510
Quantum Physics
9. What is the maximum kinetic energy in eV of a photoelectron emitted from a surface whose work function
is 5.0 eV when the surface is illuminated by radiation of 200 nm wavelength?
( h  6.626  10 34 J  s; c  3.00  10 8 m / s; e  1.60  10 19 C)
a. 1.89
b. 1.2
c. 3.1
d. zero
e. 6.2
ANS: b
10. The maximum kinetic energy of photoelectrons depends on
a. the frequency of the light.
b. the intensity of the light.
c. the number of photons that reach the surface per second.
d. the number of quanta.
e. the speed of light.
ANS: a
11. Photoelectric current magnitude depends on
a. light frequency.
b. light wavelength.
c. light speed.
d. index of refraction.
e. light intensity.
ANS: e
12. In the photoelectric effect, K max and f are
a. inversely proportional.
b. directly proportional to the square of f.
c. inverse square.
d. linearly related.
e. not related.
ANS: d
13. A sodium surface is bombarded by photons that have a wavelength of 200 nm. Find the energy of the
photons. ( h  6.626  10 34 J s ; 1 eV  1.602  10 19 J; c  3.00  108 m / s )
a. 9.23  10 19
b. 9.94  10 19
c. 7.69  10 19
d. 8.87  10 19
e. 9.54  10 19
ANS: b
Chapter 28
511
512
Quantum Physics
14. A sodium surface is bombarded by photons that have a wavelength of 200 nm. Given that   2.46 eV ,
find the cutoff wavelength in m. ( h  6.626  10 34 J s ; 1 eV  1.602  10 19 J; c 3.00 108 m / s )
a. 3.02  10 7
b. 4.17  10 7
c. 4.56  10 7
d. 5.05  10 7
e. 5.11  10 7
ANS: d
15. A sodium surface is bombarded by photons that have a wavelength of 200 nm. Given that   2.46 eV ,
find the energy of the photons in eV. ( h  6.626  10 34 J s ; 1 eV  1.602  10 19 J; c  3.00  108 m / s )
a. 1.72
b. 2.63
c. 3.75
d. 5.80
e. 6.21
ANS: e
16. The momentum of a photon of frequency f is given by
a. mv.
b. mvr.
c. hf/c.
d. hf/m.
e. hc/f.
ANS: c
17. The Compton wavelength of the electron is
a. h/mc.
b. m/f.
c. fc/m.
d. mhc/f.
e. f/rm.
ANS: a
18. The existence of wave properties of matter was first postulated by
a. Born.
b. Einstein.
c. Compton.
d. deBroglie.
e. Planck.
ANS: d
Chapter 28
513
19. The de Broglie wavelength of a particle is given by
a. h/mv.
b. cv/m.
c. h/mc.
d. mc/v.
e. hf/mv.
ANS: a
20. The frequency of matter waves is expressed in the relation f 
a. hf.
b. E/h.
c. 1/T.
d. 2 .
e.  / 2 .
ANS: b
21. Angular momentum conservation in the hydrogen atom is expressed in the relation
a. nvr = mh.
b. mvr = mh.
c. 2mvr = nh.
d. mvr = 2nh.
e. mvh = 2rn.
ANS: c
22. X-rays of wavelength  0  0.21 nm are incident on a block of material. Scattered X-rays are observed at an
angle of 40 to the incident X-ray beam. What is  in m? ( m e  9.11  10 31 kg ; h  6.626  10 34 J s ;
c  3.00  108 m / s ).
a. 5.67  10 13
b. 3.31  10 13
c. 5.86  10 13
d. 5.21  10 13
e. 6.11  10 13
ANS: a
23. X-rays of wavelength  0  0.21 nm are incident on a block of material. Scattered X-rays are observed at an
angle of 40 to the incident X-ray beam. What is the fraction of its energy that is lost by the photon?
( m e  9.11  10 31 kg ; h  6.626  10 34 J s ; c  3.00  108 m / s )
a. 2.7  10 3
b. 1.3  10 3
c. 2.9  10 3
d. 3.1  10 3
e. 3.3  10 3
514
Quantum Physics
ANS: a
Chapter 28
515
24. X-rays of wavelength  0  0.21 nm are incident on a block of material. Scattered X-rays are observed at an
angle of 40 to the incident X-ray beam. What is the wavelength of the scattered X-rays? ( m e  9.11  10 31 kg ;
h  6.626  10 34 J s ; c  3.00  108 m / s )
a. 2.10463  10 10
b. 2.10543  10 10
c. 2.10567  10 10
d. 2.10661  10 10
e. 2.10581  10 10
ANS: c
25. What is the wavelength in m of an electron that has a speed of 1.6  10 7 m/s? ( m e  9.11  10 31 kg ;
h  6.626  10 34 J s ) (Ignore relativistic corrections.)
a. 4.32  10 11
b. 5.11  10 11
c. 4.51  10 11
d. 4.50  10 11
e. 4.55  10 11
ANS: e
26. What is the wavelength in m of a proton that has a speed of 1.6  10 7 m/s? ( m e  1.67  10 27 kg ;
h  6.626  10 34 J s )
a. 2.32  10 14
b. 2.48  10 14
c. 1.79  10 14
d. 1.98  10 14
e. 2.01  10 14
ANS: b
27. The speed of an electron is 6.00  10 3 m/s  0.003%. Within what distance in m could its position be
determined if its mass is 9.11 x 10 31 kg and h  6.626  10 34 Js?
a. 3.15  10 4
b. 3.27  10 4
c. 3.29  10 4
d. 3.22  10 4
e. 3.97  10 4
ANS: d
516
Quantum Physics
28. The speed of an electron is 6.00  10 3 m/s ± 0.003%. What is its uncertainty in momentum in kgm/s?
( m e  9.11  10 31 kg )
a. 1.12  10 31
b. 1.89  10 31
c. 1.59  10 31
d. 1.33  10 31
e. 1.64  10 31
ANS: e
29. The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy
of 2 eV. The light intensity is doubled. The maximum kinetic energy of the photoelectron in eV is
a. 4.
b. 2.
c. 2 .
d. 3.
e. 16.
ANS: b
30. The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons
with a maximum kinetic energy of 2 eV. The frequency of the light is doubled. The maximum kinetic energy
in eV is
a. 3.
b. 2.
c. 2 .
d. 4.
e. 7.
ANS: e
31. A photon whose energy is 8  10 15 J is scattered off an electron at an angle of 90°. What is the wavelength
of the scattered wave in m? ( m e  9.11  10 31 kg ; h  6.626  10 34 J s ; c  3.00  108 m / s ; e  1.60  10 19 C )
a. 2.73  10 11
b. 2.25  10 11
c. 2.50  10 11
d. 2.40  10 11
e. 2.48  10 11
ANS: a
Chapter 28
517
32. A photon whose wavelength is 5.0  10 11 m is scattered straight backward after colliding with an
electron. What is the wavelength of the scattered wave in m? ( m e  9.11  10 31 kg ; h  6.626  10 34 J s ;
c  3.00  108 m / s ; e  1.60  10 19 C )
a. 5.0  10 11
b. 4.5  10 11
c. 5.5  10 11
d. 6.0  10 11
e. 6.5  10 11
ANS: c
33. A photon collides with an electron. After the collision the wavelength of the scattered photon is
a. greater than or equal to the initial wavelength.
b. equal to the initial wavelength.
c. less than or equal to the initial wavelength.
d. greater than the initial wavelength.
e. less or greater depending on the scattering angle.
ANS: a
34. What is the energy in J of one photon of AM radiation when the frequency of the radiation is 63 kHz?
( h  6.626  10 34 J s )
a. 1.0  10 38
b. 6.6  10 30
c. 4.2  10 29
d. 3.1  10 30
e. 13.1  10 29
ANS: c
35. What is the energy in J of one photon of FM radiation when the frequency of the radiation is 89.7 MHz?
( h  6.626  10 34 J s )
a. 2.2  10 33
b. 9.5  10 27
c. 7.4  10 42
d. 5.9  10 26
e. 3.7  10 25
ANS: d
518
Quantum Physics
36. An electron is moving at a speed of 2.1  10 6 m/s in the first Bohr orbit. Its deBroglie wavelength in m is
( h  6.626  10 34 Js; m e  9.11  10 31 kg )
a. 0.3  10 10
b. 1.7  10 10
c. 0.5  10 10
d. 3.5  10 10
e. 1.5  10 10
ANS: d
37. A neutron has a mass of 1.67  10 27 kg. The deBroglie wavelength is 1.4  10 10 m. How fast in m/s is the
neutron going? ( h  6.626  10 34 Js)
a. 3.4  10 3
b. 2.8  10 3
c. 3.9  10 3
d. 2.6  10 3
e. 1.7  10 3
ANS: b
38. A neutron has a mass of 1.67  10 27 kg. Its deBroglie wavelength is 1.4  10 10 m. What is its kinetic
energy in eV? ( h  6.626  10 34 Js; e  1.60  10 19 C )
a. 4
b. 0.4
c. 0.04
d. 40
e. 0.08
ANS: c
39. A neutron has a mass of 1.67  10 27 kg. Its deBroglie wavelength is 1.4  10 10 m. What is the temperature
in ºC of a gas having an average kinetic energy per molecule that is the same as the kinetic energy of the
neutron? ( h  6.626  10 34 Js; kB  1.38  10 23 J / K )
a. 273
b. 25
c. 36
d. 309
e. 51
ANS: e
Chapter 28
519
40. An electron is accelerated through a potential difference of 25,000 V. What is the wavelength of the
electron in m if relativistic efforts are ignored? ( h  6.626  10 34 Js; c  3.00  0 8 m/s; m e  9.11  10 31 kg )
a. 5.9  10 12
b. 6.8  10 12
c. 6.5  10 12
d. 7.8  10 12
e. 5.5  10 12
ANS: d
41. Which type of hot body radiation requires the highest temperature?
a. Infrared
b. Blue
c. Red
d. Yellow
e. Green
ANS: b
42.  max T  0.2898  10 2 m•K is called
a. the ultraviolet catastrophe.
b. Planck’s constant.
c. Wagner’s criterion.
d. black-body radiation constant.
e. Wien’s Displacement Law.
ANS: e
43. A person’s skin temperature is 37°C. What is the maximum wavelength of the emitted radiation in m?
a. 9.35  10 6
b. 7.83  10 6
c. 1.42  10 4
d. 0.233  10 7
e. 9.38  10 4
ANS: a
44. An oscillating system has energy 3.0 J and frequency 440 Hz. If h  6.626  10 34 Js; what is the quantum
number, n?
a. 1.29
b. 1.03  10 31
c. 2.75  10 31
d. 9.72  10 32
e. 2.03  10 6
ANS: b
520
Quantum Physics
45. What is the energy associated with a one quantum change if h  6.626  10 34 Js and f  444 Hz?
a. 3.00  10 31
b. 2.94  10 6
c. 2.94  10 31
d. 7.87  10 3
e. 4.92  10 29
ANS: c
46. The photoelectric effect was first discovered by
a. Planck.
b. Hertz.
c. Born.
d. Einstein.
e. Compton.
ANS: b
47. Which of the following uses quantum tunneling?
a. Super conductors
b. Alpha decay
c. Scan tunneling microscope
d. Both b and c
e. All of the above
ANS: d
48. According to deBroglie, which of the following objects can be thought of as exhibiting wave-particle
duality?
a. A duck
b. A car
c. An electron
d. A house
e. All of the above
ANS: e
49. Light can be thought of as both a wave and a(n)
a. fluid.
b. attractor.
c.  particle.
d. electron.
e. photon.
ANS: e
Chapter 28
50. The event predicted by the classical theory of black-body radiation as  decreases is
a. spontaneous photon emission.
b. the ultraviolet catastrophe.
c. thermal agitation.
d. tunneling.
e. the photoelectric effect.
ANS: b
51. At what frequency of light does the photoelectric effect begin?
a. Work frequency
b. 10 3 m
c. Quantum frequency
d. Stopping frequency
e. Cutoff frequency
ANS: e
52. In a graph of K max versus frequency in the photoelectric effect, the slope of the line is
a. h.
b. e.
c. 1.
d. .
e. /2.
ANS: a
53. What is the deBroglie wavelength of a 635 kg cow flying through the air at 5 m/s? ( h  6.626  10 34 Js)
a. 2.09  10 37 m
b. 2.13  10 38 m
c. 2.11  10 37 m
d. 5.22  10 36 m
e. 5.00  10 36 m
ANS: a
54. Heinsenberg’s uncertainty principle states that it is fundamentally impossible to make simultaneous
measurements, with infinite accuracy, of a particle’s position and
a. wavelength.
b. work function.
c. momentum.
d. terminal velocity.
e. quantum number.
ANS: c
521
522
Quantum Physics
55. The wave and particle characteristics of light are demonstrated
a. in the photoelectric effect.
b. in the Compton effect.
c. in single slit diffraction.
d. in double slit interference.
e. only in separate experiments.
ANS: e
56. When electrons interact with a double slit,
a. each electron passes through only one of the slits.
b. each electron scatters from the sides of only one of the slits.
c. each electron passes through both of the slits simultaneously.
d. the diffraction pattern shows up on photographic film at the screen only when lead foil is placed in front of
the film.
e. the diffraction pattern shows up on photographic film at the screen only when the electron intensity is low.
ANS: c
57. A motivation for using a wave function to represent a probability amplitude is the fact that the intensity of
an electromagnetic wave is proportional to
a. the electric field amplitude.
b. the magnetic field amplitude.
c. the square of the electric field amplitude.
d. the square root of the electric field amplitude.
e. the square root of the magnetic field amplitude.
ANS: c
58. The probability of finding a particle in volume dV surrounding a point with coordinates x, y, and z is
a.  ( x , y , z ) .
b.
2
 (x , y , z) .
c.  ( x , y , z )dV .
2
d.  ( x , y , z ) dV .
e.  ( x , y , z ) dV .
ANS: d
59. A particle in a one-dimensional infinite potential well is known as a particle in a box. When the walls of
the well are located at x  0 and x  L , the wave function of the particle must have the values  (0)  _____
and  (L)  _____.
a. 0, 0
b. 0, L
c. L, 0
d. 0, L
e. L , L
Chapter 28
ANS: a
523
524
Quantum Physics
60. A particle in a one-dimensional infinite potential well is known as a particle in a box. When the walls of
the well are located at x  0 and x  L , the particle must have wavelength   _____ if the boundary
conditions at the wall are to be satisfied.
a. 0
b. L/2
c. L/2n
d. L/n
e. 2L/n
ANS: e
61. A particle in a one-dimensional infinite potential well is known as a particle in a box. When the walls of
the well are located at x  0 and x  L , the particle must have momentum mv  _____ if the boundary
conditions at the wall are to be satisfied.
a. 0
b. 2h / L
c. 2hn / L
d. hn / L
e. hn / 2L
ANS: e
62. For a solution,  ( x ) , of the Schrödinger equation to be physically meaningful, it must
a. be single valued.
d ( x )
b. have a derivative
that is continuous for finite values of U ( x ) .
dx
c. approach zero as x approaches  .
d. have all the properties listed above.
e. have only properties (a) and (c) listed above.
ANS: d
63. In the quantum phenomenon of tunneling through a potential energy barrier, the “barrier” consists of
a. an attractive potential across a finite region of space.
b. a repulsive potential across a finite region of space.
c. an attractive potential across an infinite region of space.
d. a repulsive potential across an infinite region of space.
e. either (a) or (b) above.
ANS: b
Chapter 28
525
64. When a particle is in a box of length L, the separation between energy levels with quantum numbers n and
n  1 is
h2
a.
.
8mL2
h 2n
b.
.
8mL2
h 2n
c.
.
4mL2
h 2 ( 2n  1)
d.
.
8mL2
h 2 (n  1) 2
e.
.
8mL2
ANS: d
65. Two particles, A and B, have the same de Broglie wavelength, but m A  m B . Their momenta, p A and p B ,
are related by
a. p A  p B .
b. p A  pB .
c. p A  p B .
m
d. p A  A pB .
mB
mB
e. p A 
pB .
mA
ANS: b
66. Two particles, A and B, have the same de Broglie wavelength, but m A  m B . Their speeds, v A and v B , are
related by
a. v A  v B .
b. v A  v B .
c. v A  v B .
d.  v A  v B .
m
e. v A  A v B .
mB
ANS: a
67. When a surface with a work function of 5.00 eV is illuminated by 400 nm wavelength photons,
photoelectrons are
a. not emitted.
b. emitted with a maximum kinetic energy of 1.89 eV.
c. emitted with a maximum kinetic energy of 3.11 eV.
d. emitted with a maximum kinetic energy of 5.00 eV.
e. not emitted, but photons of 5.00 eV energy are emitted.
ANS: a.
526
Quantum Physics
Chapter 28
68. If a photon has a 640 nm wavelength, the energy of the photon in eV is
a. 4.2  10 40 .
b. 2.6  10 21.
c. 3.1  10 19
d. 1.9.
e. 3.2.
ANS: d
69. If the intensity illuminating a surface is increased while a frequency high enough to produce
photoelectrons is held fixed,
a. more photoelectrons are emitted.
b. each electron has a greater kinetic energy than with the lower illumination.
c. the cutoff frequency is decreased.
d. (a) and (b) are correct.
e. (a), (b) and (c) are correct.
ANS: a
70. The maximum change in wavelength in photons scattering from electrons occurs when the photon’s
scattering angle is
a. 0.
b. 45.
c. 90.
d. 180.
e. 270.
ANS: d
71. A particle restricted to L  x  L has a wave function ( x ) defined within that region. The integral
L
z
2
( x ) dx will be equal to
L
a. 1.
b. L.
c. 2L.
d. L2 .
L2
e.
.
2
ANS: a
527
528
Quantum Physics
72. A particle restricted to L  x  L has a wave function ( x ) defined within that region. The probability of
finding the particle described by this wave function in the region L  x  L is
1
a.
.
2L
1
b. .
L
c. 1.
d. L.
e. 2L.
ANS: c
73. A particle restricted to L  x  L has a wave function ( x ) defined within that region. The average
position, x , of the particle can be calculated from
L
a.
z
z
z
z
z
2
( x ) dx .
L
L
b.
( x )dx .
L
L
c.
2
x ( x ) dx .
L
L
d.
x ( x )dx .
L
L
e.
1
2
( x ) dx .
x
L
ANS: c
74. A particle restricted to L  x  L has a wave function ( x ) defined within that region. If the potential is
U  0 in that region, the average position, x , of the particle in this region is
a. 0.
b. 1.
L
c. .
2
d. L.
e. 2L .
ANS: a
75. A 1.0 g particle traveling at a speed of 2.0  10 4 m/s has an associated wavelength, in m, of
a. 3.32  10 35 .
b. 1.33  10 35 .
c. 3.32  10 32 .
d. 1.33  10 29 .
e. 2  10 2 .
ANS: a
Chapter 28
529
530
Quantum Physics
76. Two surfaces, A and B, are illuminated by light of wavelength . Both surfaces emit photoelectrons. If the
stopping potential of A,  A , is twice the stopping potential of B,  B , then the kinetic energies K A and K B of
the photoelectrons are related by
a. K A  K B .
b. K B  K A   A .
c. K B  K A   B .
d. K A  K B   A .
e. K A  K B   B .
ANS: b