Question 1

Probability: The square of the wave function of a particle, |ψ(x)|2, gives the probability of finding the particle at the point x.

Accepted Answer

A) True 
 B)False  False

Question 2

Particle in a box: One fairly crude method of determining the size of a molecule is to treat the molecule as an infinite square well (a box) with an electron trapped inside, and to measure the wavelengths of emitted photons. If the photon emitted during the n = 2 to n = 1 transition has wavelength 1940 nm, what is the width of the molecule? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  1.33 nm 
B)  1.12 nm 
C)  1.21 nm 
D)  1.45 nm 
A)  1.33 nm 
B)  1.12 nm 
C)  1.21 nm 
D)  1.45 nm A

Question 3

Harmonic oscillator: A lithium atom, mass 1.17 × 10-26 kg, vibrates with simple harmonic motion in a crystal lattice, where the effective force constant of the forces on the atom is k =   (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, ħ = 1.055 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
(a) What is the ground state energy of this system, in eV?
(b) What is the wavelength of the photon that could excite this system from the ground state to the first excited state?

Accepted Answer

_(a)2.14 × 10^-2_eV _(b)2.91 × 10^-5_m

Question 4

Tunneling: A 3.10-eV electron is incident on a 0.40-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  1.4 × 10-3 
B)  9.0 × 10-4 
C)  1.0 × 10-3 
D)  1.5 × 10-3 
E)  1.2 × 10-3 
A)  1.4 × 10-3 
B)  9.0 × 10-4 
C)  1.0 × 10-3 
D)  1.5 × 10-3 
E)  1.2 × 10-3

Question 5

Particle in a box: An electron in an infinite potential well (a box) makes a transition from the n = 3 level to the ground state and in so doing emits a photon of wavelength 20.9 nm. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)
(a) What is the width of this well?
(b) What wavelength photon would be required to excite the electron from its original level to the next higher one?

Accepted Answer

(a) 0.225

Question 6

Particle in a box: The lowest energy level of a particle confined to a one-dimensional region of space (a box, or infinite well) with fixed length L is E0. If an identical particle is confined to a similar region with fixed length L/ 6, what is the energy of the lowest energy level that the particles have in common? Express your answer in terms of E0.

Accepted Answer

Question 7

Particle in a box: A particle trapped in a one-dimensional finite potential well with U0 = 0 in the region 0 0 everywhere else, has a ground state wavenumber, k. The ground state wavenumber for the same particle in an infinite one-dimensional potential well of width L, would be

Accepted Answer

A)  less than k. 
B)  greater than k. 
C)  equal to k. 
D)  There is not enough information to determine. 
A)  less than k. 
B)  greater than k. 
C)  equal to k. 
D)  There is not enough information to determine.

Question 8

Three dimensional potential well: Model a hydrogen atom as a three-dimensional potential well with U0 = 0 in the region 0 -10 m. Which of the following is NOT one of the lowest three energy levels of an electron in this model?

Accepted Answer

A)  113 eV 
B)  226 eV 
C)  283 eV 
D)  339 eV 
A)  113 eV 
B)  226 eV 
C)  283 eV 
D)  339 eV

Question 9

Quantum enganglement: Two entangled fermions each have equal probabilities of being in one of two states (state 1 or state 2). The fermions are separated so that no forces act between them. One of the fermions is then studied and found to be in state 1. What is the probability that, when studied, the second particle will also be found in state 1?

Accepted Answer

A)  0% 
B)  33% 
C)  50% 
D)  67% 
E)  100% 
A)  0% 
B)  33% 
C)  50% 
D)  67% 
E)  100%

Question 10

Harmonic oscillator: The energy of a particle in the second EXCITED state of a harmonic oscillator potential is   What is the classical angular frequency of oscillation of this particle? (1 eV = 1.60 × 10-19 J, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  3.31 × 1015 rad/s 
B)  2.08 × 1016 rad/s 
C)  4.97 × 1015 rad/s 
D)  6.95 × 1015 rad/s 
A)  3.31 × 1015 rad/s 
B)  2.08 × 1016 rad/s 
C)  4.97 × 1015 rad/s 
D)  6.95 × 1015 rad/s

Question 11

Tunneling: The energy of a proton is 1.0 MeV below the top of a 1.2-MeV-high energy barrier that is 6.8 fm wide. What is the probability that the proton will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mproton = 1.67 × 10-27 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  11% 
B)  9.1% 
C)  14% 
D)  7.5% 
A)  11% 
B)  9.1% 
C)  14% 
D)  7.5%

Question 12

Tunneling: An 80-eV electron impinges upon a potential barrier 100 eV high and 0.20 nm thick. What is the probability the electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mproton = 1.67 × 10-27 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  0.027% 
B)  2.7% 
C)  0.27% 
D)  2.8 × 10-4 % 
E)  2.0 × 10-9 % 
A)  0.027% 
B)  2.7% 
C)  0.27% 
D)  2.8 × 10-4 % 
E)  2.0 × 10-9 %

Question 13

Particle in a box: A one-dimensional finite potential well has potential energy U0 = 0 in the region 0 0 = 15 eV everywhere else. A particle with which of the energies listed below would be localized (trapped) within the potential well? (Select all correct answers.)

Accepted Answer

A)  5 eV 
B)  20 eV 
C)  16 eV 
D)  7 eV 
E)  None of the above. 
A)  5 eV 
B)  20 eV 
C)  16 eV 
D)  7 eV 
E)  None of the above.

Question 14

Harmonic oscillator: Find the wavelength of the photon emitted during the transition from the second EXCITED state to the ground state in a harmonic oscillator with a classical frequency of   (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  4.03 μm 
B)  2.26 μm 
C)  2.98 μm 
D)  5.24 μm 
A)  4.03 μm 
B)  2.26 μm 
C)  2.98 μm 
D)  5.24 μm

Question 15

Harmonic oscillator: The lowest energy level of a certain quantum harmonic oscillator is 5.00 eV. What is the energy of the next higher level?

Accepted Answer

A)  7.50 eV 
B)  10.0 eV 
C)  15.0 eV 
D)  20.0 eV 
E)  50.0 eV 
A)  7.50 eV 
B)  10.0 eV 
C)  15.0 eV 
D)  20.0 eV 
E)  50.0 eV

Question 16

Particle in a box: An electron is trapped in an infinite square well (a box) of width   Find the wavelength of photons emitted when the electron drops from the n = 5 state to the n = 1 state in this system. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  6.49 μm 
B)  5.45 μm 
C)  5.91 μm 
D)  7.07 μm 
A)  6.49 μm 
B)  5.45 μm 
C)  5.91 μm 
D)  7.07 μm

Question 17

Particle in a box: An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the   to the   state, what is the wavelength of the emitted photon? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  880 nm 
B)  750 nm 
C)  610 nm 
D)  1000 nm 
E)  1100 nm 
A)  880 nm 
B)  750 nm 
C)  610 nm 
D)  1000 nm 
E)  1100 nm

Question 18

Particle in a box: You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10-18 J. What should be the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  0.11 nm 
B)  0.22 nm 
C)  0.15 nm 
D)  0.18 nm 
A)  0.11 nm 
B)  0.22 nm 
C)  0.15 nm 
D)  0.18 nm

Question 19

Normalization: A set of five possible wave functions is given below, where L is a positive real number. ψ1(x) = Ae-x, for all x ψ2(x) = A cos x, for all x
Ψ3(x) =   ψ4(x) =   ψ5(x) =   Which of the five possible wave functions are normalizable? (There may be more than one correct choice.)

Accepted Answer

A)  ψ1(x) 
B)  ψ2(x) 
C)  ψ3(x) 
D)  ψ4(x) 
E)  ψ5(x) 
A)  ψ1(x) 
B)  ψ2(x) 
C)  ψ3(x) 
D)  ψ4(x) 
E)  ψ5(x)

Question 20

Particle in a box: An electron is in the ground state of an infinite well (a box) where its energy is 5.00 eV. In the next higher level, what would its energy be? (1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  1.25 eV 
B)  2.50 eV 
C)  10.0 eV 
D)  15.0 eV 
E)  20.0 eV 
A)  1.25 eV 
B)  2.50 eV 
C)  10.0 eV 
D)  15.0 eV 
E)  20.0 eV

Exam 31: Alternating Current

Probability: The square of the wave function of a particle, |ψ(x)|2, gives the probability of finding the particle at the point x.

Tunneling: A 3.10-eV electron is incident on a 0.40-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Particle in a box: A particle trapped in a one-dimensional finite potential well with U0 = 0 in the region 0 < x < L, and finite U0 everywhere else, has a ground state wavenumber, k. The ground state wavenumber for the same particle in an infinite one-dimensional potential well of width L, would be

Harmonic oscillator: The energy of a particle in the second EXCITED state of a harmonic oscillator potential is What is the classical angular frequency of oscillation of this particle? (1 eV = 1.60 × 10-19 J, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Tunneling: The energy of a proton is 1.0 MeV below the top of a 1.2-MeV-high energy barrier that is 6.8 fm wide. What is the probability that the proton will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mproton = 1.67 × 10-27 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Tunneling: An 80-eV electron impinges upon a potential barrier 100 eV high and 0.20 nm thick. What is the probability the electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mproton = 1.67 × 10-27 kg, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Particle in a box: A one-dimensional finite potential well has potential energy U0 = 0 in the region 0 < x < 0.2 nm, and U0 = 15 eV everywhere else. A particle with which of the energies listed below would be localized (trapped) within the potential well? (Select all correct answers.)

Harmonic oscillator: Find the wavelength of the photon emitted during the transition from the second EXCITED state to the ground state in a harmonic oscillator with a classical frequency of (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, ħ = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Harmonic oscillator: The lowest energy level of a certain quantum harmonic oscillator is 5.00 eV. What is the energy of the next higher level?

Particle in a box: An electron is trapped in an infinite square well (a box) of width Find the wavelength of photons emitted when the electron drops from the n = 5 state to the n = 1 state in this system. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Particle in a box: An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the to the state, what is the wavelength of the emitted photon? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19 J)

Particle in a box: You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10-18 J. What should be the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Normalization: A set of five possible wave functions is given below, where L is a positive real number. ψ1(x) = Ae-x, for all x ψ2(x) = A cos x, for all x Ψ3(x) = ψ4(x) = ψ5(x) = Which of the five possible wave functions are normalizable? (There may be more than one correct choice.)

Particle in a box: An electron is in the ground state of an infinite well (a box) where its energy is 5.00 eV. In the next higher level, what would its energy be? (1 eV = 1.60 × 10-19 J)

Motion Along a Straight Line

Motion in Two or Three Dimensions

Newtons Laws of Motion

Applying Newtons Laws

Work and Kinetic Energy

Potential Energy and Energy Conservation

Momentum, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Fluid Mechanics

Gravitation

Periodic Motion

Mechanical Waves

Sound and Hearing

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic Field

Electromagnetic Induction

Inductance

Electromagnetic Waves Optics

The Nature and Propagation of Light

Geometric Optics

Interference

Filters

Probability: The square of the wave function of a particle, |ψ(x)|², gives the probability of finding the particle at the point x.

Tunneling: A 3.10-eV electron is incident on a 0.40-nm barrier that is 5.67 eV high. What is the probability that this electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, m_el = 9.11 × 10^-31 kg, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Harmonic oscillator: The energy of a particle in the second EXCITED state of a harmonic oscillator potential is What is the classical angular frequency of oscillation of this particle? (1 eV = 1.60 × 10^-19 J, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Tunneling: An 80-eV electron impinges upon a potential barrier 100 eV high and 0.20 nm thick. What is the probability the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, m_proton = 1.67 × 10^-27 kg, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Particle in a box: A one-dimensional finite potential well has potential energy U₀= 0 in the region 0 < x < 0.2 nm, and U₀= 15 eV everywhere else. A particle with which of the energies listed below would be localized (trapped) within the potential well? (Select all correct answers.)

Harmonic oscillator: Find the wavelength of the photon emitted during the transition from the second EXCITED state to the ground state in a harmonic oscillator with a classical frequency of (c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Particle in a box: An electron is trapped in an infinite square well (a box) of width Find the wavelength of photons emitted when the electron drops from the n = 5 state to the n = 1 state in this system. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg)

Particle in a box: An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the to the state, what is the wavelength of the emitted photon? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19^J)

Particle in a box: You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10^-18 J. What should be the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

Normalization: A set of five possible wave functions is given below, where L is a positive real number. ψ₁(x) = Ae^-^x, for all x ψ₂(x) = A cos x, for all x Ψ₃(x) = ψ₄(x) = ψ5(x) = Which of the five possible wave functions are normalizable? (There may be more than one correct choice.)

Particle in a box: An electron is in the ground state of an infinite well (a box) where its energy is 5.00 eV. In the next higher level, what would its energy be? (1 eV = 1.60 × 10^-19 J)