11th Edition Test Bank Answers Ch.39 More About Matter Waves - Fundamentals of Physics 11e Complete Test Bank by David Halliday. DOCX document preview.
Chapter: Chapter 39
Learning Objectives
LO 39.1.0 Solve problems related to energies of a trapped electron.
LO 39.1.1 Identify the confinement principle: Confinement of a wave (including a matter wave) leads to the quantization of wavelengths and energy values.
LO 39.1.2 Sketch a one-dimensional infinite potential well, indicating the length (or width) and the potential energy of the walls.
LO 39.1.3 For an electron, apply the relationship between the de Broglie wavelength λ and the kinetic energy.
LO 39.1.4 For an electron in a one-dimensional infinite potential well, apply the relationship between the de Broglie wavelength λ, the well’s length, and the quantum number n.
LO 39.1.5 For an electron in a one-dimensional infinite potential well, apply the relationship between the allowed energies En, the well length L, and the quantum number n.
LO 39.1.6 Sketch an energy-level diagram for an electron in a one-dimensional infinite potential well, indicating the ground state and several excited states.
LO 39.1.7 Identify that a trapped electron tends to be in its ground state, can be excited to a higher energy state, and cannot exist between the allowed states.
LO 39.1.8 Calculate the energy change required for an electron to move between states: a quantum jump up or down an energy-level diagram.
LO 39.1.9 If a quantum jump involves light, identify that an upward jump requires the absorption of a photon (to increase the electron’s energy) and a downward jump requires the emission of a photon (to reduce the electron’s energy).
LO 39.1.10 If a quantum jump involves light, apply the relationships between the energy change and the frequency and wavelength associated with the photon.
LO 39.1.11 Identify the emission and absorption spectra of an electron in a one-dimensional infinite potential well.
LO 39.2.0 Solve problems related to wave functions of a trapped electron.
LO 39.2.1 For an electron trapped in a one-dimensional, infinite potential well, write its wave function in terms of coordinates inside the well and in terms of the quantum number n.
LO 39.2.2 Identify probability density.
LO 39.2.3 For an electron trapped in a one-dimensional, infinite potential well in a given state, write the probability density as a function of position inside the well, identify that the probability density is zero outside the well, and calculate the probability of detection between two given coordinates inside the well.
LO 39.2.4 Identify the correspondence principle.
LO 39.2.5 Normalize a given wave function and identify what that has to do with the probability of detection.
LO 39.2.6 Identify that the lowest allowed energy (the zero-point energy) of a trapped electron is not zero.
LO 39.3.0 Solve problems related to an electron in a finite well.
LO 39.3.1 Sketch a one-dimensional finite potential well, indicating the length and height.
LO 39.3.2 For an electron trapped in a finite well with given energy levels, sketch the energy-level diagram, indicate the nonquantized region, and compare the energies and de Broglie wavelengths with those of an infinite well of the same length.
LO 39.3.3 For an electron trapped in a finite well, explain (in principle) how the wave functions for the allowed states are determined
LO 39.3.4 For an electron trapped in a finite well with a given quantum number, sketch the probability density as a function of position across the well and into the walls
LO 39.3.5 Identify that a trapped electron can exist in only the allowed states and relate that energy of the state to the kinetic energy of the electron.
LO 39.3.6 Calculate the energy that an electron must absorb or emit to move between the allowed states or between an allowed state and any value in the nonquantized region.
LO 39.3.7 If a quantum jump involves light, apply the relationship between the energy change and the frequency and wavelength associated with the photon.
LO 39.3.8 From a given allowed state in a finite well, calculate the minimum energy required for the electron to escape and the kinetic energy of the escaped electron if provided more than that minimal energy.
LO 39.3.9 Identify the emission and absorption spectra of an electron in a one-dimensional infinite potential well.
LO 38.4.0 Solve problems related to two- and three-dimensional electron traps.
LO 39.4.1 Discuss nanocrystallites as being electron traps and explain how their threshold wavelength can determine their color.
LO 39.4.2 Identify quantum dots and quantum corrals.
LO 39.4.3 For a given state of an electron in an infinite potential well with two or three dimensions, write equations for the wave function and probability density and then calculate the probability of detection for a given range in the well.
LO 39.4.4 For a given state of an electron in an infinite potential well with two or three dimensions, calculate the allowed energies and draw an energy-level diagram, complete with labels for the quantum numbers, the ground state, and several excited states.
LO 39.4.5 Identify degenerate states
LO 39.4.6 Calculate the energy that an electron must absorb or emit to move between the allowed states in a 2D or 3D trap.
LO 39.4.7 If a quantum jump involves light, apply the relationships between the energy change and the frequency and wavelength associated with the photon.
LO 39.5.0 Solve problems related to the hydrogen atom.
LO 39.5.1 Identify Bohr’s model of the hydrogen atom and explain how he derived the quantized radii and energies.
LO 39.5.2 For a given quantum number n in the Bohr model, calculate the electron’s orbital radius, kinetic energy, potential energy, total energy, orbital period, orbital frequency, momentum, and angular momentum.
LO 39.5.3 Distinguish the Bohr and Schrӧdinger descriptions of the hydrogen atom, including the discrepancy between the allowed angular momentum values.
LO 39.5.4 For a hydrogen atom, apply the relationship between the quantized energies En and the quantum number n.
LO 39.5.5 For a given jump in hydrogen, between quantized states or between a quantized state and a nonquantized state, calculate the change in energy and, if light is involved, the associated energy, frequency, wavelength, and momentum of the photon.
LO 39.5.6 Sketch an energy-level diagram for hydrogen, identifying the ground state, several of the excited states, the nonquantized region, the Paschen series, the Balmer series, and the Lyman series (including the series limits).
LO 39.5.7 For each transition series, identify the jumps giving the longest wavelength, the shortest wavelength (for downward jumps), the series limit, and ionization.
LO 39.5.8 List the quantum numbers for an atom and indicate the allowed values.
LO 39.5.9 Given a normalized wave function for a state, find the radial probability density P(r) and the probability of detecting the electron in a given range of radii.
LO 39.5.10 For ground-state hydrogen, sketch a graph of the radial probability density versus radial distance and locate one Bohr radius a.
LO 39.5.11 For a given normalized wave function for hydrogen, verify that it satisfies the Schrӧdinger equation.
LO 39.5.12 Distinguish shell from subshell.
LO 39.5.13 Explain a dot plot of the probability density for a given state.
Multiple Choice
1. An electron confined in a one-dimensional infinite potential well has an energy of 180 eV. What is its wavelength?
A) 65 pm
B) 91 pm
C) 130 pm
D) 370 pm
E) 520 pm
Difficulty: M
Section: 39-1
Learning Objective 39.1.3
2. The wavelength 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/n2
D)
E) n2
Difficulty: E
Section: 39-1
Learning Objective 39.1.4
3. 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/n2
D)
E) n2
Difficulty: E
Section: 39-1
Learning Objective 39.1.5
4. 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) 0.5 eV
B) 1.0 eV
C) 2.0 eV
D) 4.0 eV
E) 8.0 eV
Difficulty: M
Section: 39-1
Learning Objective 39.1.5
5. An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. The ratio E3/E1 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
Difficulty: E
Section: 39-1
Learning Objective 39.1.5
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 = 2L0, n = 2 |
2. L = 2L0, n = 4 |
3. L = 3L0, n = 3 |
4. L = 4L0, 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, then 4
D) 4, then 1 and 3 tied, then 2
E) 2, then 1 and 3 tied, then 4
Difficulty: M
Section: 39-1
Learning Objective 39.1.5
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 = 4m0, width = 2L0 | |
2. mass = 2m0, width = 2L0 | |
3. mass = 4m0, width = L0 | |
4. mass = m0, width = 2L0 |
Rank them according to the kinetic energies of the particles when they are in their ground states, lowest to highest.
A) 3 and 4 tied, then 2, then 1
B) 1, 2, then 3 and 4 tied
C) 1 and 2 tied, then 3, then 4
D) 4, 3, 2, 1
E) 3, 1, 2, 4
Difficulty: M
Section: 39-1
Learning Objective 39.1.5
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
Difficulty: E
Section: 39-1
Learning Objective 39.1.5
9. 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
Difficulty: M
Section: 39-1
Learning Objective 39.1.5
10. 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
Difficulty: M
Section: 39-1
Learning Objective 39.1.5
11. A particle is trapped in a one-dimensional well with infinite 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
Difficulty: M
Section: 39-1
Learning Objective 39.1.8
12. An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:
A) 5.4 107 m
B) 3.0 107 m
C) 1.7 107 m
D) 1.2 107 m
E) 1.0 107 m
Difficulty: M
Section: 39-1
Learning Objective 39.1.10
13. An electron in an atom drops from an energy level at –1.1 10–18 J to an energy level at –2.4 10–18 J. The wave associated with the emitted photon has a frequency of:
A) 2.0 1017 Hz
B) 2.0 1015 Hz
C) 2.0 1013 Hz
D) 2.0 1011 Hz
E) 2.0 109 Hz
Difficulty: M
Section: 39-1
Learning Objective 39.1.10
14. An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. The momentum of the photon is:
A) 1.7 10–27 kg m/s
B) 2.3 10–27 kg m/s
C) 4.0 10–27 kg m/s
D) 5.7 10–27 kg m/s
E) 8.0 10–27 kg m/s
Difficulty: M
Section: 39-1
Learning Objective 39.1.10
15. 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 (x) versus x is shown. The value of quantum number n is:
A) 0
B) 1
C) 2
D) 4
E) 8
Difficulty: E
Section: 39-2
Learning Objective 39.2.1
16. 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 probability density P(x) versus x is shown. The value of the quantum number n is:
A) 0
B) 1
C) 2
D) 3
E) 4
Difficulty: E
Section: 39-2
Learning Objective 39.2.3
17. 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) 0
B) 7
C) 13
D) 14
E) 15
Difficulty: E
Section: 39-2
Learning Objective 39.2.3
18. 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) 0
B) 7
C) 13
D) 14
E) 15
Difficulty: E
Section: 39-2
Learning Objective 39.2.3
19. 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
Difficulty: M
Section: 39-2
Learning Objective 39.2.3
20. If a wave function for a particle moving along the x axis is "normalized" then:
A) 2dt = 1
B) 2dx = 1
C) /x = 1
D) /t = 1
E) 2 = 1
Difficulty: E
Section: 39-2
Learning Objective 39.2.5
21. 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
Difficulty: E
Section: 39-3
Learning Objective 39.3.0
22. A particle is confined by finite potential energy walls to a one-dimensional trap from
x = 0 to x = L. Its wave function in the region x > L has the form:
A) (x) = A sin(kx)
B) (x) = Aekx
C) (x) = Ae–kx
D) (x) = Aeikx
E) (x) = 0
Difficulty: E
Section: 39-3
Learning Objective 39.3.0
23. 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
Difficulty: E
Section: 39-3
Learning Objective 39.3.0
24. 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) 0
B) 1
C) 3
D) 4
E) 5
Difficulty: E
Section: 39-3
Learning Objective 39.3.4
25. The figure shows the energy levels for an electron in a finite potential energy well. If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon?
A) 6.0 nm
B) 5.7 nm
C) 5.3 nm
D) 3.0 nm
E) 2.3 nm
Difficulty: M
Section: 39-3
Learning Objective 39.3.6
26. The figure shows the energy levels for an electron in a finite potential energy well. If an electron in the n = 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron?
A) It makes a transition to the n = 3 state.
B) It makes a transition to the n = 4 state.
C) It escapes the well with a kinetic energy of 280 eV.
D) It escapes the well with a kinetic energy of 730 eV.
E) Nothing; this photon does not have an energy corresponding to an allowed transition so it is not absorbed.
Difficulty: M
Section: 39-3
Learning Objective 39.3.9
27. An electron is trapped in an infinitely deep rectangular well with sides of length Lx = L and Ly = 2L. The energy of the state nx = 2, ny = 4 is:
A)
B)
C)
D)
E)
Difficulty: M
Section: 39-4
Learning Objective 39.4.4
28. An electron is trapped in an infinitely deep rectangular well with sides of length Lx = L and Ly = 2L. The energy that the electron needs to move from the ground state to the state nx = 2, ny = 4 is:
A)
B)
C)
D)
E)
Difficulty: M
Section: 39-4
Learning Objective 39.4.6
29. The quantum number n is most closely associated with what property of the electron in a hydrogen atom?
A) Energy
B) Orbital angular momentum
C) Spin angular momentum
D) Magnetic moment
E) z component of angular momentum
Difficulty: E
Section: 39-5
Learning Objective 39.5.0
30. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is –13.6 eV. The minus sign indicates:
A) the kinetic energy is negative
B) the potential energy is positive
C) the electron might escape from the atom
D) the electron and proton are bound together
E) none of the above
Difficulty: E
Section: 39-5
Learning Objective 39.5.0
31. The wave function for an electron in a state with zero angular momentum:
A) is zero everywhere
B) is spherically symmetric
C) depends on the angle from the z axis
D) depends on the angle from the x axis
E) is spherically symmetric for some shells and depends on the angle from the z axis for others
Difficulty: E
Section: 39-5
Learning Objective 39.5.0
32. Consider the following:
I. | the probability density for an ℓ = 0 state | ||
II. | the probability density for a state with ℓ ≠ 0 | ||
III. | the average of the probability densities for all states in an ℓ ≠ 0 subshell |
Of these which are spherically symmetric?
A) only I
B) only II
C) only I and II
D) only I and III
E) I, II, and III
Difficulty: E
Section: 39-5
Learning Objective 39.5.0
33. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then, according to the quantum theory the energy En of a state with principal quantum number n is proportional to:
A) n
B) n2
C) 1/n
D) 1/n2
E) none of the above
Difficulty: E
Section: 39-5
Learning Objective 39.5.2
34. The binding energy of an electron in the ground state in a hydrogen atom is about:
A) 1.0 eV
B) 3.4 eV
C) 10.2 eV
D) 13.6 eV
E) 27.2 eV
Difficulty: E
Section: 39-5
Learning Objective 39.5.4
35. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is –13.6 eV. The energy of the first excited state is:
A) 0 eV
B) –3.4 eV
C) –6.8 eV
D) –10.2 eV
E) –27 eV
Difficulty: M
Section: 39-5
Learning Objective 39.5.4
36. Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is –13.6 eV. When the electron is in the first excited state its excitation energy (the difference between the energy of the state and that of the ground state) is:
A) 0
B) 3.4 eV
C) 6.8 eV
D) 10.2 eV
E) 13.6 eV
Difficulty: M
Section: 39-5
Learning Objective 39.5.4
37. The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?
A) I
B) II
C) III
D) IV
E) V
Difficulty: E
Section: 39-5
Learning Objective 39.5.5
38. When a hydrogen atom makes the transition from the second excited state to the ground state (at –13.6 eV) the energy of the photon emitted is:
A) 0 eV
B) 1.5 eV
C) 9.1 eV
D) 12.1 eV
E) 13.6 eV
Difficulty: E
Section: 39-5
Learning Objective 39.5.5
39. The series limit for the Balmer series represents a transition m n, where (m, n) is
A) (2,1)
B) (3,2)
C) (,0)
D) (,1)
E) (,2)
Difficulty: E
Section: 39-5
Learning Objective 39.5.7
40. The Balmer series of hydrogen is important because it:
A) is the only one for which the Bohr theory can be used
B) is the only series which occurs for hydrogen
C) is in the visible region
D) involves the lowest possible quantum number n
E) involves the highest possible quantum number n
Difficulty: E
Section: 39-5
Learning Objective 39.5.7
41. Which of the following sets of quantum numbers is possible for an electron in a hydrogen atom?
A) n = 4, ℓ = 3, mℓ = −3
B) n = 4, ℓ = 4, mℓ = −2
C) n = 5, ℓ = −1, mℓ = 2
D) n = 3, ℓ = 1, mℓ = −2
E) n = 2, ℓ = 3, mℓ = −2
Difficulty: E
Section: 39-5
Learning Objective 39.5.8
42. If the wave function is spherically symmetric then the radial probability density is given by:
A) 4r2
B) 2
C) 4r22
D) 42
E) 4r2
Difficulty: E
Section: 39-5
Learning Objective 39.5.9
43. If P(r) is the radial probability density for a hydrogen atom then the probability that the separation of the electron and proton is between r and r + dr is:
A) P dr
B) P 2 dr
C) 4r2P dr
D) 4r2P dr
E) 4P dr
Difficulty: E
Section: 39-5
Learning Objective 39.5.9
44. The radial probability density for the electron in the ground state of a hydrogen atom has a peak at about:
A) 0.5 pm
B) 5 pm
C) 50 pm
D) 500 pm
E) 5000 pm
Difficulty: E
Section: 39-5
Learning Objective 39.5.10
45. The following image is a dot plot of the ground state of the hydrogen atom. The dots represent:
A) all the possible positions of the electron
B) every electron in the atom
C) the electron wave function
D) the volume probability density for the electron
E) the density of the electron cloud
Difficulty: E
Section: 39-5
Learning objective 39.5.13