Question 1

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many maxima does the probability density have?

Accepted Answer

A) 0 
B) 7 
C) 13 
D) 14 
E) 15 
A) 0 
B) 7 
C) 13 
D) 14 
E) 15 D

Question 2

Consider the following:   Of these which are spherically symmetric?

Accepted Answer

A) only I 
B) only II 
C) only I and II 
D) only I and III 
E) I, II, and III 
A) only I 
B) only II 
C) only I and II 
D) only I and III 
E) I, II, and III D

Question 3

A particle is trapped in a one-dimensional well with infinite potential energy at the walls.Three possible pairs of energy levels are   Order these pairs according to the difference in energy, least to greatest.

Accepted Answer

A) 1, 2, 3 
B) 3, 2, 1 
C) 2, 3, 1 
D) 1, 3, 2 
E) 3, 1, 2 
A) 1, 2, 3 
B) 3, 2, 1 
C) 2, 3, 1 
D) 1, 3, 2 
E) 3, 1, 2 C

Question 4

The figure shows the energy levels for an electron in a finite potential energy well.If an electron in the n = 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron?

Accepted Answer

A) It makes a transition to the n = 3 state. 
B) It makes a transition to the n = 4 state. 
C) It escapes the well with a kinetic energy of 280 eV. 
D) It escapes the well with a kinetic energy of 730 eV. 
E) Nothing; this photon does not have an energy corresponding to an allowed transition so it is not absorbed. 
A) It makes a transition to the n = 3 state. 
B) It makes a transition to the n = 4 state. 
C) It escapes the well with a kinetic energy of 280 eV. 
D) It escapes the well with a kinetic energy of 730 eV. 
E) Nothing; this photon does not have an energy corresponding to an allowed transition so it is not absorbed.

Question 5

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.A graph of its wave function    (x)versus x is shown.The value of quantum number n is:

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 4 
E) 8 
A) 0 
B) 1 
C) 2 
D) 4 
E) 8

Question 6

If the wave function     is spherically symmetric then the radial probability density is given by:

Accepted Answer

A) "4  $\pi$  r2   " 
B)   
C)   
D)   
E)   
A) "4  $\pi$  r2   " 
B)   
C)   
D)   
E)

Question 7

A particle is confined to a one-dimensional trap by infinite potential energy walls.Of the following states, designed by the quantum number n, for which one is the probability density greatest near the center of the well?

Accepted Answer

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

Question 8

If a wave function     for a particle moving along the x axis is "normalized" then:

Accepted Answer

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

Question 9

If P(r)is the radial probability density for a hydrogen atom then the probability that the separation of the electron and proton is between r and r + dr is:

Accepted Answer

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

Question 10

The following image is a dot plot of the ground state of the hydrogen atom.The dots represent:

Accepted Answer

A) all the possible positions of the electron 
B) every electron in the atom 
C) the electron wave function 
D) the volume probability density for the electron 
E) the density of the electron cloud 
A) all the possible positions of the electron 
B) every electron in the atom 
C) the electron wave function 
D) the volume probability density for the electron 
E) the density of the electron cloud

Question 11

Four different particles are trapped in one-dimensional wells with infinite potential energy at their walls.The masses of the particles and the width of the wells are   Rank them according to the kinetic energies of the particles when they are in their ground states, lowest to highest.

Accepted Answer

A) 3 and 4 tied, then 2, then 1 
B) 1, 2, then 3 and 4 tied 
C) 1 and 2 tied, then 3, then 4 
D) 4, 3, 2, 1 
E) 3, 1, 2, 4 
A) 3 and 4 tied, then 2, then 1 
B) 1, 2, then 3 and 4 tied 
C) 1 and 2 tied, then 3, then 4 
D) 4, 3, 2, 1 
E) 3, 1, 2, 4

Question 12

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.The ratio E3/E1 of the energy for n = 3 to that for n = 1 is:

Accepted Answer

A) 1/3 
B) 1/9 
C) 3/1 
D) 9/1 
E) 1/1 
A) 1/3 
B) 1/9 
C) 3/1 
D) 9/1 
E) 1/1

Question 13

Identical particles are trapped in one-dimensional wells with infinite potential energy at the walls.The widths L of the traps and the quantum numbers n of the particles are   Rank them according to the kinetic energies of the particles, least to greatest.

Accepted Answer

A) 1, 2, 3, 4 
B) 4, 3, 2, 1 
C) 1 and 3 tied, then 2, then 4 
D) 4, then 1 and 3 tied, then 2 
E) 2, then 1 and 3 tied, then 4 
A) 1, 2, 3, 4 
B) 4, 3, 2, 1 
C) 1 and 3 tied, then 2, then 4 
D) 4, then 1 and 3 tied, then 2 
E) 2, then 1 and 3 tied, then 4

Question 14

An electron is in a one-dimensional well with finite potential energy barriers at the walls.The matter wave:

Accepted Answer

A) is zero at the barriers 
B) is zero everywhere within each barrier 
C) is zero in the well 
D) extends into the barriers 
E) is discontinuous at the barriers 
A) is zero at the barriers 
B) is zero everywhere within each barrier 
C) is zero in the well 
D) extends into the barriers 
E) is discontinuous at the barriers

Question 15

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is 2.0 eV.If the width of the well is doubled, the ground state energy will be:

Accepted Answer

A) 0.5 eV 
B) 1.0 eV 
C) 2.0 eV 
D) 4.0 eV 
E) 8.0 eV 
A) 0.5 eV 
B) 1.0 eV 
C) 2.0 eV 
D) 4.0 eV 
E) 8.0 eV

Question 16

An electron is trapped in an infinitely deep rectangular well with sides of length Lx = L and Ly = 2L.The energy that the electron needs to move from the ground state to the state nx = 2, ny = 4 is:

Accepted Answer

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

Question 17

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls:

Accepted Answer

A) is zero 
B) decreases with temperature 
C) increases with temperature 
D) is independent of temperature 
E) oscillates with time 
A) is zero 
B) decreases with temperature 
C) increases with temperature 
D) is independent of temperature 
E) oscillates with time

Question 18

An electron in an atom initially has an energy 7.5 eV above the ground state energy.It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process.The momentum of the photon is:

Accepted Answer

A) 1.7 * 10-27 kg .m/s 
B) 2.3 * 10-27 kg . m/s 
C) 4.0* 10-27 kg . m/s 
D) 5.7 *10-27 kg . m/s 
E) 8.0 * 10-27 kg . m/s 
A) 1.7 * 10-27 kg .m/s 
B) 2.3 * 10-27 kg . m/s 
C) 4.0* 10-27 kg . m/s 
D) 5.7 *10-27 kg . m/s 
E) 8.0 * 10-27 kg . m/s

Question 19

The series limit for the Balmer series represents a transition m $\rightarrow$ n, where (m, n)is

Accepted Answer

A) (2,1) 
B) (3,2) 
C) ($\infty$,0) 
D) ($\infty$,1) 
E) ($\infty$,2) 
A) (2,1) 
B) (3,2) 
C) ($\infty$,0) 
D) ($\infty$,1) 
E) ($\infty$,2)

Question 20

The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number):

Accepted Answer

A) n 
B) 1/n 
C) 1/n2 
D)    
E) n2 
A) n 
B) 1/n 
C) 1/n2 
D)    
E) n2

Exam 39: More About Matter Waves

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many maxima does the probability density have?

Consider the following: Of these which are spherically symmetric?

A particle is trapped in a one-dimensional well with infinite potential energy at the walls.Three possible pairs of energy levels are Order these pairs according to the difference in energy, least to greatest.

The figure shows the energy levels for an electron in a finite potential energy well.If an electron in the n = 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron?

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.A graph of its wave function (x)versus x is shown.The value of quantum number n is:

If the wave function is spherically symmetric then the radial probability density is given by:

A particle is confined to a one-dimensional trap by infinite potential energy walls.Of the following states, designed by the quantum number n, for which one is the probability density greatest near the center of the well?

If a wave function for a particle moving along the x axis is "normalized" then:

If P(r)is the radial probability density for a hydrogen atom then the probability that the separation of the electron and proton is between r and r + dr is:

The following image is a dot plot of the ground state of the hydrogen atom.The dots represent:

Four different particles are trapped in one-dimensional wells with infinite potential energy at their walls.The masses of the particles and the width of the wells are Rank them according to the kinetic energies of the particles when they are in their ground states, lowest to highest.

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.The ratio E3/E1 of the energy for n = 3 to that for n = 1 is:

Identical particles are trapped in one-dimensional wells with infinite potential energy at the walls.The widths L of the traps and the quantum numbers n of the particles are Rank them according to the kinetic energies of the particles, least to greatest.

An electron is in a one-dimensional well with finite potential energy barriers at the walls.The matter wave:

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is 2.0 eV.If the width of the well is doubled, the ground state energy will be:

An electron is trapped in an infinitely deep rectangular well with sides of length Lx = L and Ly = 2L.The energy that the electron needs to move from the ground state to the state nx = 2, ny = 4 is:

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls:

An electron in an atom initially has an energy 7.5 eV above the ground state energy.It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process.The momentum of the photon is:

The series limit for the Balmer series represents a transition m →\rightarrow→ n, where (m, n)is

The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number):

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An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.The ratio E₃/E₁ of the energy for n = 3 to that for n = 1 is:

An electron is trapped in an infinitely deep rectangular well with sides of length L_x = L and L_y = 2L.The energy that the electron needs to move from the ground state to the state n_x = 2, n_y = 4 is:

The series limit for the Balmer series represents a transition m $\rightarrow$ n, where (m, n)is