Halliday D., Resnick R., Walker J. Fundamentals of physics. Test Bank
Подождите немного. Документ загружается.
34. Monoenergetic electrons are incident on a single slit barrier. If the energy of each incident
electron is increased the central maximum of the diffraction pattern:
A. widens
B. narrows
C. stays the same width
D. widens for slow electrons and narrows for fast electrons
E. narrows for slow electrons and widens for fast electrons
ans: B
35. A free electron and a free proton have the same kinetic energy. This means that, compared to
the matter wave associated with the proton, the matter wave associated with the electron has:
A. a shorter wavelength and a greater frequency
B. a longer wavelength and a greater frequency
C. a shorter wavelength and the same frequency
D. a longer wavelength and the same frequency
E. a shorter wavelength and a smaller frequency
ans: D
36. A free electron and a free proton have the same momentum. This means that, compared to
the matter wave associated with the proton, the matter wave asso ciated with the electron:
A. has a shorter wavelength and a greater frequency
B. has a longer wavelength and a greater frequency
C. has the same wavelength and the same frequency
D. has the same wavelength and a greater frequency
E. has the same wavelength and a smaller frequency
ans: D
37. A free electron and a free proton have the same speed. This means that, compared to the
matter wave associated with the proton, the matter wave associated with the electron:
A. has a shorter wavelength and a greater frequency
B. has a longer wavelength and a greater frequency
C. has the same wavelength and the same frequency
D. has the same wavelength and a greater frequency
E. has a longer wavelength and a smaller frequency
ans: E
38. Consider the following three particles:
1. a free electron with speed v
0
2. a free proton with speed v
0
3. a free proton with speed 2 v
0
Rank them according to the wavelengths of their matter waves, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 1, then 2 and 3 tied
ans: B
Chapter 38: PHOTONS AND MATTER WAVES 581
39. Consider the following three particles:
1. a free electron with kinetic energy K
0
2. a free proton with kinetic energy K
0
3. a free proton with kinetic energy 2K
0
Rank them according to the wavelengths of their matter waves, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 1, then 2 and 3 tied
ans: B
40. A free electron has a momentum of 5.0 × 10
−24
kg · m/s. The wavelength of its wave function
is:
A. 1.3 × 10
−8
m
B. 1.3 × 10
−10
m
C. 2.1 × 10
−11
m
D. 2.1 × 10
−13
m
E. none of these
ans: B
41. The frequency and wavelength of the matter wave associated with a 10-eV free electron are:
A. 1.5 × 10
34
Hz, 3.9 × 10
−10
m
B. 1.5 × 10
34
Hz, 1.3 × 10
−34
m
C. 2.4 × 10
15
Hz, 1.2 × 10
−9
m
D. 2.4 × 10
15
Hz, 3.9 × 10
−10
m
E. 4.8 × 10
15
Hz, 1.9 × 10
−10
m
ans: D
42. If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave function
changes by the factor:
A. 1/
√
2
B. 1/2
C. 1/4
D.
√
2
E. 2
ans: E
43. A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kinetic
energy is:
A. 4K
B. 2K
C. still K
D. K/2
E. K/4
ans: E
582 Chapter 38: PHOTONS AND MATTER WAVES
44. The probability that a particle is in a given small region of space is proportional to:
A. its energy
B. its momentum
C. the frequency of its wave function
D. the wavelength of its wave function
E. the square of the magnitude of its wave function
ans: E
45. ψ(x) is the wave function for a particle moving along the x axis. The probability that the
particle is in the interval from x = a to x = b is given by:
A. ψ(b) − ψ(a)
B. |ψ(b)|/|ψ(a)|
C. |ψ(b)|
2
/|ψ(a)|
2
D.
$
b
a
ψ(x) dx
E.
$
b
a
|ψ(x)|
2
dx
ans: E
46. The significance of |ψ|
2
is:
A. probability
B. energy
C. probability density
D. energy density
E. wavelength
ans: C
47. Maxwell’s equations are to electric and magnetic fields as
equation is to the wave function
for a particle.
A. Einstein’s
B. Fermi’s
C. Newton’s
D. Schr¨odinger’s
E. Bohr’s
ans: D
48. A free electron in motion along the x axis has a localized wave function. The uncertainty in
its momentum is decreased if:
A. the wave function is made more narrow
B. the wave function is made less narrow
C. the wave function remains the same but the energy of the electron is increased
D. the wave function remains the same but the energy of the electron is decreased
E. none of the above
ans: B
Chapter 38: PHOTONS AND MATTER WAVES 583
49. The uncertainty in position of an electron in a certain state is 5 × 10
−10
m. The uncertainty in
its momentum might be:
A. 5.0 × 10
−24
kg · m/s
B. 4.0 × 10
−24
kg · m/s
C. 3.0 × 10
−24
kg · m/s
D. all of the above
E. none of the above
ans: D
50. The reflection coefficient R for a certain barrier tunneling problem is 0.80. The corresponding
transmission coefficient T is:
A. 0.80
B. 0.60
C. 0.50
D. 0.20
E. 0
ans: D
51. An electron with energy E is incident upon a potential energy barrier of height E
pot
>Eand
thickness L. The transmission coefficient T :
A. is zero
B. decreases exponentially with L
C. is proportional to 1/L
D. is proportional to 1/L
2
E. is non-zero and independent of L
ans: B
52. In order to tunnel through a potential barrier a particle must:
A. have energy greater than the barrier height
B. have spin
C. be massive
D. have a wavelength longer than the barrier width
E. none of the above
ans: E
53. An electron with energy E is incident on a potential energy barrier of height E
pot
and thickness
L. The probability of tunneling increases if:
A. E decreases without any other changes
B. E
pot
increases without any other changes
C. L decreases without any other changes
D. E and E
pot
increase by the same amount
E. E and E
pot
decrease by the same amount
ans: C
584 Chapter 38: PHOTONS AND MATTER WAVES
54. Identical particles, each with energy E, are incident on the following four potential energy
barriers:
1. barrier height = 5E, barrier width = 2L
2. barrier height = 10E, barrier width = L
3. barrier height = 17E, barrier width = L/2
4. barrier height = 26E, barrier width = L/3
Rank the barriers in terms of the probability that the particles tunnel through them, from least
probability to greatest probability.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1 and 2 tied, then 3, then 4
D. 2, then 1 and 3 tied, then 4
E. 3, 2, 1, 4
ans: A
Chapter 38: PHOTONS AND MATTER WAVES 585
Chapter 39: MORE ABOUT MATTER WAVES
1. If a wave function ψ for a particle moving along the x axis is normalized, then:
A.
$
|ψ|
2
dt =1
B.
$
|ψ|
2
dx =1
C. ∂ψ/∂x =1
D. ∂ψ/∂t =1
E. |ψ|
2
=1
ans: B
2. The energy of a particle in a one-dimensional trap with zero potential energy in the interior
and infinite potential energy at the walls is proportional to (n = quantum number):
A. n
B. 1/n
C. 1/n
2
D.
√
n
E. n
2
ans: E
3. The ground state energy of an electron in a one-dimensional trap with zero potential energy
in the interior and infinite potential energy at the walls is 2.0 eV. If the width of the well is
doubled, the ground state energy will be:
A. 0.5eV
B. 1.0eV
C. 2.0eV
D. 4.0eV
E. 8.0eV
ans: A
4. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite
potential energy at the walls. The ratio E
3
/E
1
of the energy for n = 3 to that for n = 1 is:
A. 1/3
B. 1/9
C. 3/1
D. 9/1
E. 1/1
ans: D
586 Chapter 39: MORE ABOUT MATTER WAVES
5. A particle is trapped in a one-dimensional well with in finite potential energy at the walls. Three
possible pairs of energy levels are
1. n = 3 and n =1
2. n = 3 and n =2
3. n = 4 and n =3
Order these pairs according to the difference in energy, least to greatest.
A. 1, 2, 3
B. 3, 2, 1
C. 2, 3, 1
D. 1, 3, 2
E. 3, 1, 2
ans: C
6. Identical particles are trapped in one-dimensional wells with infinite potential energy at the
walls. The widths L of the traps and the quantum numbers n of the particles are
1. L =2L
0
, n =2
2. L =2L
0
, n =4
3. L =3L
0
, n =3
4. L =4L
0
, n =2
Rank them according to the kinetic energies of the particles, least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1 and 3 tied, then 2, 4
D. 4, 2, then 1 and 3 tied
E. 1, 3, then 2 and 4 tied
ans: D
7. Four different particles are trapped in one-dimensional wells with infinite potential energy at
their walls. The masses of the particles and the width of the wells are
1. mass = 4m
0
, width = 2L
0
2. mass = 2m
0
, width = 2L
0
3. mass = 4m
0
, width = L
0
4. mass = m
0
, width = 2L
0
Rank them according to the kinetic energies of the particles when they are in their ground
states.
A. 1, 2, 3, 4
B. 1, 2, 3 and 4 tied
C. 1 and 2 tied, then 3, 4
D. 4, 3, 2, 1
E. 3, 1, 2, 4
ans: B
Chapter 39: MORE ABOUT MATTER WAVES 587
8. The ground state energy of an electron in a one-dimensional trap with zero potential energy in
the interior and infinite potential energy at the walls:
A. is zero
B. decreases with temperature
C. increases with temperature
D. is independent of temperature
E. oscillates with time
ans: D
9. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite
potential energy at the walls. A graph of its wave function ψ(x) versus x is shown. The value
of quantum number n is:
x
ψ
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
A. 0
B. 2
C. 4
D. 6
E. 8
ans: C
10. An electron is in a one-dimensional trap with zero potential energy in the interior and in finite
potential energy at the walls. A graph of its probability density P (x) versus x is shown. The
value of the quantum number n is:
x
P
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
A. 0
B. 1
C. 2
D. 3
E. 4
ans: C
588 Chapter 39: MORE ABOUT MATTER WAVES
11. A particle is trapped in an infinite potential energy well. It is in the state with quantum
number n = 14. How many nodes does the probability density have (counting the nodes at the
ends of the well)?
A. none
B. 7
C. 13
D. 14
E. 15
ans: E
12. A particle is trapped in an infinite potential energy well. It is in the state with quantum
number n = 14. How many maxima does the probability density have?
A. none
B. 7
C. 13
D. 14
E. 15
ans: D
13. A particle is confined to a one-dimensional trap by infinite potential energy walls. Of the
following states, designed by the quantum number n, for which one is the probability density
greatest near the center of the well?
A. n =2
B. n =3
C. n =4
D. n =5
E. n =6
ans: B
14. Two one-dimensional traps have infinite potential energy at their walls Trap A has width L
and trap B has width 2L. For which value of the quantum number n does a particle in trap B
have the same energy as a particle in the ground state of trap A?
A. n =1
B. n =2
C. n =3
D. n =4
E. n =5
ans: B
15. An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum
number n = 3 its kinetic energy is:
A. 6.0 × 10
−28
J
B. 1.8 × 10
−27
J
C. 6.7 × 10
−19
J
D. 2.0 × 10
−18
J
E. 6.0 × 10
−18
J
ans: E
Chapter 39: MORE ABOUT MATTER WAVES 589
16. An electron is in a one-dimensional well with finite potential energy barriers at the walls. The
matter wave:
A. is zero at the barriers
B. is zero everywhere within each barrier
C. is zero in the well
D. extends into the barriers
E. is discontinuous at the barriers
ans: D
17. A particle is confined by finite potential energy walls to a one-dimensional trap from x =0to
x = L. Its wave function in the region x>Lhas the form:
A. ψ(x)=A sin(kx)
B. ψ(x)=Ae
kx
C. ψ(x)=Ae
−kx
D. ψ(x)=Ae
ikx
E. ψ(x)=0
ans: C
18. A particle is trapped in a finite potential energy well that is deep enough so that the electron
can be in the state with n = 4. For this state how many nodes does the probability density
have?
A. none
B. 1
C. 3
D. 5
E. 7
ans: C
19. A particle in a certain finite potential energy well can have any of five quantized energy values
and no more. Which of the following would allow it to have any of six quantized energy levels?
A. Increase the momentum of the particle
B. Decrease the momentum of the particle
C. Decrease the well width
D. Increase the well depth
E. Decrease the well depth
ans: D
20. A particle in a certain finite potential energy well can have any of five quantized energy values
and no more. Which of the following would allow it to have any of six quantized energy levels?
A. Increase the energy of the particle
B. Decrease the energy of the particle
C. Make the well shallower
D. Make the well deeper
E. Make the well narrower
ans: D
590 Chapter 39: MORE ABOUT MATTER WAVES