Question 1

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, h = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)   0.56%
B)   0.35%
C)   0.40%
D)   0.25%
E)   0.48%

Question 2

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 × 10⁻³⁴J ∙ 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 3

An electron is confined in a harmonic oscillator potential well. A photon is emitted when the electron undergoes a 3→1 quantum jump. What is the wavelength of the emission if the net force on the electron behaves as though it has a spring constant of 9.6 N/m? (mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J,   = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)  A)  290 nm B)  150 nm C)  190 nm D)  580 nm" class="answers-bank-image d-inline" rel="preload" > = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)   290 nm
B)   150 nm
C)   190 nm
D)   580 nm A

Question 4

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. The mass of a nickel atom is 9.75 × 10-26 kg. What is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 J ∙ s, 13 rad/s. The mass of a nickel atom is 9.75 × 10-26 kg. What is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 J ∙ s,   = 1.055 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)  A)  0.015 eV B)  0.019 eV C)  0.023 eV D)  0.027 eV E)  0.031 eV" class="answers-bank-image d-inline" rel="preload" > = 1.055 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)

Accepted Answer

A)   0.015 eV
B)   0.019 eV
C)   0.023 eV
D)   0.027 eV
E)   0.031 eV

Question 5

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well)  in which you can do this? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)   5.5 µm
B)   11 µm
C)   2.8 µm
D)   1.4 µm

Question 6

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)   43
B)   44
C)   45
D)   42
E)   41

Question 7

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)   1.9 nm
B)   0.93 nm
C)   1.1 nm
D)   2.3 nm A

Question 8

The wave function for a particle must be normalizable because

Accepted Answer

A)   the particle's momentum must be conserved.
B)   the particle's angular momentum must be conserved.
C)   the particle's charge must be conserved.
D)   the particle must be somewhere.
E)   the particle cannot be in two places at the same time.

Question 9

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

Question 10

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, -19 J, mproton = 1.67 × 10-27 kg,   = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)  A)  11% B)  9.1% C)  14% D)  7.5%" class="answers-bank-image d-inline" rel="preload" > = 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%

Question 11

An electron is trapped in an infinite square well (a box)  of width 6.88 nm. 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, mel = 9.11 × 10-31 kg)

Accepted Answer

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

Question 12

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

Question 13

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 × 10-34J ∙ 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

Question 14

The wave function for an electron that is confined to x ≥ 0 nm is
ψ(x) =  
(a) What must be the value of b?
(b) What is the probability of finding the electron in a 0.010 nm-wide region centered at x = 1.0 nm?

Accepted Answer

(a) 0.56 (...

Question 15

An electron is in an infinite square well (a box)  that is 2.0 nm wide. The electron makes a transition from the n = 8 to the n = 7 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)

Accepted Answer

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

Question 16

If an atom in a crystal is acted upon by a restoring force that is directly proportional to the distance of the atom from its equilibrium position in the crystal, then it is impossible for the atom to have zero kinetic energy.

Accepted Answer

A) True 
 B)False

Question 17

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 18

The smallest kinetic energy that an electron in a box (an infinite well) can have is zero.

Accepted Answer

A) True 
 B)False

Question 19

A particle is confined to a one-dimensional box (an infinite well)  on the x-axis between x = 0 and x = L. The potential height of the walls of the box is infinite. The normalized wave function of the particle, which is in the ground state, is given by ψ(x)  =  sin 
, with 0 ≤ x ≤ L. What is the probability of finding the particle between x = 0 and x = L/3?

Accepted Answer

A)   0.20
B)   0.22
C)   0.24
D)   0.26
E)   0.28

Question 20

Calculate the ground state energy of a harmonic oscillator with a classical frequency of 3.68 × 1015 Hz. (1 eV = 1.60 × 10-19 J, h = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)   7.62 eV
B)   15.2 eV
C)   11.4 eV
D)   5.71 eV

Exam 39: Quantum Mechanics

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, h = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
verified

Correct Answer
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(a) 0.225 ...
View Answer

Correct Answer
verified
A

Correct Answer
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You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

Correct Answer
verified

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

Correct Answer
verified

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J. What is the length of the box? (h = 6.626 × 10-³⁴ J ∙ s, ^mel = 9.11 × 10^-31 kg)

Correct Answer
verified
A

The wave function for a particle must be normalizable because

Correct Answer
verified

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)

Correct Answer
verified

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, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
verified

An electron is trapped in an infinite square well (a box) of width 6.88 nm. 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, ^mel = 9.11 × 10^-31 kg)

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified
A

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x) = (a) What must be the value of b? (b) What is the probability of finding the electron in a 0.010 nm-wide region centered at x = 1.0 nm?

Correct Answer
verified
(a) 0.56 (...
View Answer

An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the n = 8 to the n = 7 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)

Correct Answer
verified

If an atom in a crystal is acted upon by a restoring force that is directly proportional to the distance of the atom from its equilibrium position in the crystal, then it is impossible for the atom to have zero kinetic energy.

Correct Answer
verified

Correct Answer
verified

The smallest kinetic energy that an electron in a box (an infinite well) can have is zero.

Correct Answer
verified

Correct Answer
verified

Calculate the ground state energy of a harmonic oscillator with a classical frequency of 3.68 × 10¹⁵ Hz. (1 eV = 1.60 × 10^-19 J, h = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
verified

Exam 39: Quantum Mechanics

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, h = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Correct AnswerverifiedShow Answer

Correct Answerverified(a) 0.225 ...View AnswerShow Answer

Correct AnswerverifiedA

Correct AnswerverifiedShow Answer

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Correct AnswerverifiedShow Answer

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Correct AnswerverifiedShow Answer

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Correct AnswerverifiedA

The wave function for a particle must be normalizable because

Correct AnswerverifiedShow Answer

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)

Correct AnswerverifiedShow Answer

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, = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Correct AnswerverifiedShow Answer

An electron is trapped in an infinite square well (a box) of width 6.88 nm. 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, mel = 9.11 × 10-31 kg)

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct AnswerverifiedA

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x) = (a) What must be the value of b? (b) What is the probability of finding the electron in a 0.010 nm-wide region centered at x = 1.0 nm?

Correct Answerverified(a) 0.56 (...View AnswerShow Answer

An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the n = 8 to the n = 7 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)

Correct AnswerverifiedShow Answer

If an atom in a crystal is acted upon by a restoring force that is directly proportional to the distance of the atom from its equilibrium position in the crystal, then it is impossible for the atom to have zero kinetic energy.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The smallest kinetic energy that an electron in a box (an infinite well) can have is zero.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Calculate the ground state energy of a harmonic oscillator with a classical frequency of 3.68 × 1015 Hz. (1 eV = 1.60 × 10-19 J, h = 1.055 × 10-34 J ∙ s, h = 6.626 × 10-34 J ∙ s)

Correct AnswerverifiedShow Answer

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, h = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
verified

Correct Answer
verified
(a) 0.225 ...
View Answer

Correct Answer
verified
A

Correct Answer
verified

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

Correct Answer
verified

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

Correct Answer
verified

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J. What is the length of the box? (h = 6.626 × 10-³⁴ J ∙ s, ^mel = 9.11 × 10^-31 kg)

Correct Answer
verified
A

Correct Answer
verified

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)

Correct Answer
verified

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, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
verified

An electron is trapped in an infinite square well (a box) of width 6.88 nm. 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, ^mel = 9.11 × 10^-31 kg)

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified
A

Correct Answer
verified
(a) 0.56 (...
View Answer

An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the n = 8 to the n = 7 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)

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Calculate the ground state energy of a harmonic oscillator with a classical frequency of 3.68 × 10¹⁵ Hz. (1 eV = 1.60 × 10^-19 J, h = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Correct Answer
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