Question 1

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)  0.0048 eV 
B)  0.0057 eV 
C)  0.0066 eV 
D)  0.0076 eV 
E)  0.0085 eV

Question 2

An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  1.4 × 10-2 
B)  2.8 × 10-2 
C)  5.5 × 10-2 
D)  1.1 × 10-2 
E)  1.4 × 10-1

Question 3

An electron is confined in a harmonic oscillator potential well. What is the longest wavelength of light that the electron can absorb if the net force on the electron behaves as though it has a spring constant of 74 N/m? (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)

Accepted Answer

A)  210 nm 
B)  200 nm 
C)  220 nm 
D)  230 nm

Question 4

The wave function of an electron in a rigid box (infinite well) is shown in the figure. If the electron energy 98.0 eV, what is the energy of the electron's ground state? ( mel = 9.11 × 10-31 kg)

Accepted Answer

A)  6.13 eV 
B)  3.92 eV 
C)  10.9 eV 
D)  24.5 eV

Question 5

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

Question 6

An electron is bound in an infinite square-well potential (a box) on the x-axis. The width of the well is L and the well extends from x = 0.00 nm to x = 3.8 nm. In its present state, the normalized wave function of the electron is given by: ψ(x) =  sin (2πx/L). What is the energy of the electron in this state? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)  0.10 eV 
B)  0.052 eV 
C)  0.13 eV 
D)  0.078 eV 
E)  0.026 eV

Question 7

Find the value of A to normalize the wave function ψ(x) =  .

Accepted Answer

A)  1/L 
B)   
C)  1/L2 
D)  1.  
E)  1/

Question 8

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 maximum probability per unit length of finding the particle?

Accepted Answer

A)  1/  
B)   
C)  2/  
D)  1/L 
E)  2/L

Question 9

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 = 49.0 N/m. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10⁻³⁴ J ∙ s, = 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

The answer of A lithium atom, mass 1.17 × 10-⁻²⁶...

Question 10

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,  = 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 %

Question 11

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 3.72 × 1013 Hz. (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)

Accepted Answer

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

Question 12

The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through the apparatus, what is the expected number that will land in a 0.10 mm-wide strip centered at x = 0.00 mm?

Accepted Answer

A)  140 
B)  1400 
C)  450 
D)  45

Question 13

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)

Question 14

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,  = 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)  4.96 × 1015 rad/s 
D)  6.95 × 1015 rad/s

Question 15

Find the value of A to normalize the wave function ψ(x) =  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

The wave function for an electron that is confined to x ≥ 0 nm is
ψ(x) =  
(a) What must be the value of A?
(b) What is the probability of finding the electron in the interval 1.15 nm ≤ x ≤ 1.84 nm?

Accepted Answer

The answer of The wave function for an electron that...

Question 17

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level En = 24.0 MeV and an adjacent energy level En+1= 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  1.50 MeV 
B)  13.5 MeV 
C)  0.500 MeV 
D)  4.50 MeV

Question 18

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

Question 19

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well). If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  8.0 × 10-64 J 
B)  3.2 × 10-46 J 
C)  1.3 × 10-20 J 
D)  zero

Question 20

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

Accepted Answer

The answer of An electron is bound in an infinite...

Exam 39: Quantum Mechanics

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, ^mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

The wave function of an electron in a rigid box (infinite well) is shown in the figure. If the electron energy 98.0 eV, what is the energy of the electron's ground state? ( ^mel = 9.11 × 10^-31 kg)

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)

Find the value of A to normalize the wave function ψ(x) = .

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

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 3.72 × 10¹³ Hz. (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)

The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through the apparatus, what is the expected number that will land in a 0.10 mm-wide strip centered at x = 0.00 mm?

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.)

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

Find the value of A to normalize the wave function ψ(x) = .

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x) = (a) What must be the value of A? (b) What is the probability of finding the electron in the interval 1.15 nm ≤ x ≤ 1.84 nm?

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level E_n = 24.0 MeV and an adjacent energy level E_n+1= 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10^-19 J)

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

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well) . If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10^-34 J ∙ s)

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

Exam 39: Quantum Mechanics

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s)

The wave function of an electron in a rigid box (infinite well) is shown in the figure. If the electron energy 98.0 eV, what is the energy of the electron's ground state? ( mel = 9.11 × 10-31 kg)

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)

Find the value of A to normalize the wave function ψ(x) = .

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

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 3.72 × 1013 Hz. (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)

The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through the apparatus, what is the expected number that will land in a 0.10 mm-wide strip centered at x = 0.00 mm?

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.)

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

Find the value of A to normalize the wave function ψ(x) = .

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x) = (a) What must be the value of A? (b) What is the probability of finding the electron in the interval 1.15 nm ≤ x ≤ 1.84 nm?

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level En = 24.0 MeV and an adjacent energy level En+1= 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10-19 J)

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

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well) . If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10-34 J ∙ s)

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, ^mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

The wave function of an electron in a rigid box (infinite well) is shown in the figure. If the electron energy 98.0 eV, what is the energy of the electron's ground state? ( ^mel = 9.11 × 10^-31 kg)

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)

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

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 3.72 × 10¹³ Hz. (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 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.)

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

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level E_n = 24.0 MeV and an adjacent energy level E_n+1= 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10^-19 J)

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well) . If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10^-34 J ∙ s)

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)