Question 1

A particle is confined in a three-dimensional box with L1 = L,L2 = 2L and L3 = 3L.The energy levels of the particle are given by

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E) None of these is correct. 
A)    . 
B)    . 
C)    . 
D)    . 
E) None of these is correct.

Question 2

A particle is in a three-dimensional box with L3 = L2 = 3L1.The lowest energy level is

Accepted Answer

A) zero 
B) 1.22E0  
C) 1.56E0  
D) 1.67E0  
E) 1.94E0  
A) zero 
B) 1.22E0  
C) 1.56E0  
D) 1.67E0  
E) 1.94E0

Question 3

A particle of mass m is confined in a two-dimensional box that has sides Lx = L and Ly = 2L.By what factor is the energy of the 3rd excited state larger than the energy of the ground state?

Accepted Answer

A) 5/4 
B) 13/5 
C) 17/4 
D) 17/5 
E) 4 
A) 5/4 
B) 13/5 
C) 17/4 
D) 17/5 
E) 4

Question 4

An electron is confined in a two-dimensional box where U(x,y)= 0 for x = 0 to L,and y = 0 to 3L,and U(x,y)= infinity outside these boundaries.If L = 0.5 nm then calculate the energy of the first doubly degenerate levels.

Accepted Answer

A) 9.9 eV 
B) 11.0 eV 
C) 8.5 eV 
D) 7.7 eV 
E) 6.2 eV 
A) 9.9 eV 
B) 11.0 eV 
C) 8.5 eV 
D) 7.7 eV 
E) 6.2 eV

Question 5

In order to solve the Schrödinger's equation,which of the following quantity(ies)must be specified?

Accepted Answer

A) the kinetic energy function of the particle 
B) the potential energy function of the particle 
C) the boundary conditions 
D) (
A) and (
B)  
E) (
B) and (
C)  
A) the kinetic energy function of the particle 
B) the potential energy function of the particle 
C) the boundary conditions 
D) (
A) and (
B)  
E) (
B) and (
C)

Question 6

Suppose the natural frequency of oscillation for H2 is $\backsim$1012 Hz and the amplitude of oscillation is $\backsim$10-12 m,the total energy of the harmonic oscillator is of the order

Accepted Answer

A) 10-20 J 
B) 10-22 J 
C) 10-24 J 
D) 10-26  J 
E) 10-28 J 
A) 10-20 J 
B) 10-22 J 
C) 10-24 J 
D) 10-26  J 
E) 10-28 J

Question 7

An electron is confined in a two-dimensional box where U(x,y)= 0 for x = 0 to L and y = 0 to 3L,and U(x,y)= infinity outside these boundaries.If L = 0.5 nm,then calculate the energy of the first excited state.

Accepted Answer

A) 1.7 eV 
B) 2.2 eV 
C) 6.2 eV 
D) 3.0 eV 
E) None of these is correct. 
A) 1.7 eV 
B) 2.2 eV 
C) 6.2 eV 
D) 3.0 eV 
E) None of these is correct.

Question 8

The probability of penetration of a rectangular barrier __________ with the square root of the relative barrier height.

Accepted Answer

A) increases linearly 
B) decreases exponentially 
C) decreases linearly 
D) increases exponentially 
E) decreases as a damped sinusoid 
A) increases linearly 
B) decreases exponentially 
C) decreases linearly 
D) increases exponentially 
E) decreases as a damped sinusoid

Question 9

The probability of penetration of a rectangular barrier ________ with the barrier thickness.

Accepted Answer

A) increases linearly 
B) decreases exponentially 
C) decreases linearly 
D) increases exponentially 
E) decreases as a damped sinusoid 
A) increases linearly 
B) decreases exponentially 
C) decreases linearly 
D) increases exponentially 
E) decreases as a damped sinusoid

Question 10

An electron of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0.The ratio of the wavelength of the transmitted wave to the incident wave is

Accepted Answer

A) 2 
B) 1 
C) 0.5 
D)    
E)    
A) 2 
B) 1 
C) 0.5 
D)    
E)

Question 11

A particle is in a three-dimensional box with L3 = L2 = 3L1.The energy level E1,1,2 is

Accepted Answer

A) zero 
B) 1.22E0  
C) 1.56E0  
D) 1.67E0  
E) 1.94E0  
A) zero 
B) 1.22E0  
C) 1.56E0  
D) 1.67E0  
E) 1.94E0

Question 12

An electron with kinetic energy 5.0 eV traveling in a region in which the potential energy is zero is incident at x > 0 on a potential barrier of height 3.0 eV.What is the wavelength of the electron in the region x > 0?

Accepted Answer

A) 0.87 nm 
B) 0.99 nm 
C) 0.54 nm 
D) 2.3 nm 
E) 0.14 nm 
A) 0.87 nm 
B) 0.99 nm 
C) 0.54 nm 
D) 2.3 nm 
E) 0.14 nm

Question 13

The number of degenerate states in the third excited state for a particle in a three-dimensional box with L1 = L2 = L3 is

Accepted Answer

A) 2 
B) 3  
C) 4  
D) 5  
E) 6  
A) 2 
B) 3  
C) 4  
D) 5  
E) 6

Question 14

The ground-state wave function of the harmonic oscillator is

Accepted Answer

A)    
B) $\varPsi$ 0(x)= A0e-ax  
C) $\varPsi$ 0(x)= A0sin(ax) 
D) $\varPsi$ 0(x)= A0sin(ax2) 
E)    
A)    
B) $\varPsi$ 0(x)= A0e-ax  
C) $\varPsi$ 0(x)= A0sin(ax) 
D) $\varPsi$ 0(x)= A0sin(ax2) 
E)

Question 15

The dependent variable in the Schrödinger equation is

Accepted Answer

A) the wave function $\varPsi$ . 
B) the position variable x. 
C) the time variable t. 
D) the potential energy function U. 
E) None of these is correct. 
A) the wave function $\varPsi$ . 
B) the position variable x. 
C) the time variable t. 
D) the potential energy function U. 
E) None of these is correct.

Question 16

The probability of penetration of a rectangular barrier decreases exponentially with the ________ of the barrier height.

Accepted Answer

A) square 
B) cube 
C) square root 
D) cube root 
E) fourth root 
A) square 
B) cube 
C) square root 
D) cube root 
E) fourth root

Question 17

A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0.What is the ratio of E0/U0 so that the reflection co-efficient is 25%? (Assume E0 is much less than the rest mass energy of the particle.)

Accepted Answer

A) 4.0 
B) 1.25 
C) 1.125 
D) 1.025 
E) 0.75 
A) 4.0 
B) 1.25 
C) 1.125 
D) 1.025 
E) 0.75

Question 18

The wave function for the energy level in a cubical box of side L that corresponds to the quantum numbers 1,2,and 3 is

Accepted Answer

A) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin(2$\pi$x/L)sin($\pi$x/L) 
B) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin($\pi$x/L)sin(3$\pi$x/L) 
C) $\varPsi$ 1,2,3 = sin(2$\pi$x/L)sin(3$\pi$x/L) 
D) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin(2$\pi$x/L)sin(3$\pi$x/L) 
E) $\varPsi$ 1,2,3 = 2A sin($\pi$x/L)sin(2$\pi$x/L)sin(3$\pi$x/L) 
A) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin(2$\pi$x/L)sin($\pi$x/L) 
B) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin($\pi$x/L)sin(3$\pi$x/L) 
C) $\varPsi$ 1,2,3 = sin(2$\pi$x/L)sin(3$\pi$x/L) 
D) $\varPsi$ 1,2,3 = A sin($\pi$x/L)sin(2$\pi$x/L)sin(3$\pi$x/L) 
E) $\varPsi$ 1,2,3 = 2A sin($\pi$x/L)sin(2$\pi$x/L)sin(3$\pi$x/L)

Question 19

Particles that have symmetric wave functions and are not subject to the Pauli exclusion principle are called

Accepted Answer

A) quarks 
B) leptons 
C) fermions 
D) bosons 
E) None of these is correct. 
A) quarks 
B) leptons 
C) fermions 
D) bosons 
E) None of these is correct.

Question 20

A particle is confined in a three-dimensional box with L1 = L2 = 3L3.The quantum numbers for the second excited state are

Accepted Answer

A) (1,1,2)and (1,2,1) 
B) (1,2,1)and (2,1,1) 
C) (2,2,1)and (2,1,2) 
D) (1,2,2)and (2,1,2) 
E) (2,2,1)and (1,2,2) 
A) (1,1,2)and (1,2,1) 
B) (1,2,1)and (2,1,1) 
C) (2,2,1)and (2,1,2) 
D) (1,2,2)and (2,1,2) 
E) (2,2,1)and (1,2,2)

Exam 35: Applications of the Schrodinger Equation

A particle is confined in a three-dimensional box with L1 = L,L2 = 2L and L3 = 3L.The energy levels of the particle are given by

A particle is in a three-dimensional box with L3 = L2 = 3L1.The lowest energy level is

A particle of mass m is confined in a two-dimensional box that has sides Lx = L and Ly = 2L.By what factor is the energy of the 3rd excited state larger than the energy of the ground state?

An electron is confined in a two-dimensional box where U(x,y)= 0 for x = 0 to L,and y = 0 to 3L,and U(x,y)= infinity outside these boundaries.If L = 0.5 nm then calculate the energy of the first doubly degenerate levels.

In order to solve the Schrödinger's equation,which of the following quantity(ies)must be specified?

Suppose the natural frequency of oscillation for H2 is ∽\backsim∽ 1012 Hz and the amplitude of oscillation is ∽\backsim∽ 10-12 m,the total energy of the harmonic oscillator is of the order

An electron is confined in a two-dimensional box where U(x,y)= 0 for x = 0 to L and y = 0 to 3L,and U(x,y)= infinity outside these boundaries.If L = 0.5 nm,then calculate the energy of the first excited state.

The probability of penetration of a rectangular barrier __________ with the square root of the relative barrier height.

The probability of penetration of a rectangular barrier ________ with the barrier thickness.

An electron of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0.The ratio of the wavelength of the transmitted wave to the incident wave is

A particle is in a three-dimensional box with L3 = L2 = 3L1.The energy level E1,1,2 is

An electron with kinetic energy 5.0 eV traveling in a region in which the potential energy is zero is incident at x > 0 on a potential barrier of height 3.0 eV.What is the wavelength of the electron in the region x > 0?

The number of degenerate states in the third excited state for a particle in a three-dimensional box with L1 = L2 = L3 is

The ground-state wave function of the harmonic oscillator is

The dependent variable in the Schrödinger equation is

The probability of penetration of a rectangular barrier decreases exponentially with the ________ of the barrier height.

A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0.What is the ratio of E0/U0 so that the reflection co-efficient is 25%? (Assume E0 is much less than the rest mass energy of the particle.)

The wave function for the energy level in a cubical box of side L that corresponds to the quantum numbers 1,2,and 3 is

Particles that have symmetric wave functions and are not subject to the Pauli exclusion principle are called

A particle is confined in a three-dimensional box with L1 = L2 = 3L3.The quantum numbers for the second excited state are

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A particle is confined in a three-dimensional box with L₁= L,L₂ = 2L and L₃ = 3L.The energy levels of the particle are given by

A particle is in a three-dimensional box with L₃ = L₂ = 3L₁.The lowest energy level is

A particle of mass m is confined in a two-dimensional box that has sides L_x = L and L_y = 2L.By what factor is the energy of the 3rd excited state larger than the energy of the ground state?

Suppose the natural frequency of oscillation for H₂ is $\backsim$ 10¹² Hz and the amplitude of oscillation is $\backsim$ 10^-1² m,the total energy of the harmonic oscillator is of the order

An electron of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.5E₀.The ratio of the wavelength of the transmitted wave to the incident wave is

A particle is in a three-dimensional box with L₃ = L₂ = 3L₁.The energy level E_1,1,2 is

The number of degenerate states in the third excited state for a particle in a three-dimensional box with L₁= L₂ = L₃ is

A particle of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U₀.What is the ratio of E₀/U₀ so that the reflection co-efficient is 25%? (Assume E₀ is much less than the rest mass energy of the particle.)

A particle is confined in a three-dimensional box with L₁= L₂ = 3L₃.The quantum numbers for the second excited state are