Question 1

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?

Accepted Answer

A)  8.0 ×   J 
B)  3.2 ×   J 
C)  1.3 ×   J 
D)  zero 
A)  8.0 ×   J 
B)  3.2 ×   J 
C)  1.3 ×   J 
D)  zero A

Question 2

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 =     ,h = 6.626 × 10-34 J • s,h = 1.055 × 10-34 J • s,   (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 3

A particle trapped in a one-dimensional finite potential well with U0 = 0 in the region   ,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

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. B

Question 4

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,   ,h = 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 5

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,   h = 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 
A)  210 nm 
B)  200 nm 
C)  220 nm 
D)  230 nm

Question 6

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

Question 7

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

(a)0.93 (n

Question 8

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   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,

Accepted Answer

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

Question 9

A particle confined in a rigid one-dimensional box (an infinite well)of length 17.0 fm has an energy level   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 
A)  1.50 MeV 
B)  13.5 MeV 
C)  0.500 MeV 
D)  4.50 MeV

Question 10

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.   ,h = 6.626 × 10-34 J ∙ s,mel = 9.11 × 10-31 kg)

Accepted Answer

Question 11

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,   ,

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

Question 12

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

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) 
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?   ,h = 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 
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

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

Question 16

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 
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 17

A particle is confined to a one-dimensional box (an infinite well)on the x-axis between   and   .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   .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 
A)  1/   
B)    
C)  2/   
D)  1/L 
E)  2/L

Question 18

A one-dimensional finite potential well has potential energy U0 = 0 in the region 0 < x < .2 nm,and   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 19

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 20

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Exam 40: Quantum Mechanics

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?

A particle trapped in a one-dimensional finite potential well with U0 = 0 in the region ,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

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, ,h = 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 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)

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. ,h = 6.626 × 10-34 J ∙ s,mel = 9.11 × 10-31 kg)

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)

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? ,h = 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?

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)

A one-dimensional finite potential well has potential energy U0 = 0 in the region 0 < x < .2 nm,and everywhere else.A particle with which of the energies listed below would be localized (trapped)within the potential well? (Select all correct answers.)

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

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Filters

A particle trapped in a one-dimensional finite potential well with U₀= 0 in the region ,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

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, ,h = 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 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)

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. ,h = 6.626 × 10^-34 J ∙ s,m_el = 9.11 × 10^-31 kg)

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)

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

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,m_el = 9.11 × 10^-31 kg,h = 6.626 × 10^-34 J • s)

A one-dimensional finite potential well has potential energy U₀= 0 in the region 0 < x < .2 nm,and everywhere else.A particle with which of the energies listed below would be localized (trapped)within the potential well? (Select all correct answers.)