Question 1

An electron confined in a one-dimensional infinite potential well has an energy of 180 eV.What is its wavelength?

Accepted Answer

A) 65 pm 
B) 91 pm 
C) 130 pm 
D) 370 pm 
E) 520 pm 
A) 65 pm 
B) 91 pm 
C) 130 pm 
D) 370 pm 
E) 520 pm B

Question 2

An electron is trapped in a deep well with a width of 0.3 nm.If it is in the state with quantum number n = 3 its kinetic energy is:

Accepted Answer

A) 6.0 * 10-28 J 
B) 1.8 *10-27 J 
C) 6.7 * 10-19 J 
D) 2.0 * 10-18 J 
E) 6.0 * 10-18 J 
A) 6.0 * 10-28 J 
B) 1.8 *10-27 J 
C) 6.7 * 10-19 J 
D) 2.0 * 10-18 J 
E) 6.0 * 10-18 J E

Question 3

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many nodes does the probability density have (counting the nodes at the ends of the well)?

Accepted Answer

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

Question 4

The Balmer series of hydrogen is important because it:

Accepted Answer

A) is the only one for which the Bohr theory can be used 
B) is the only series which occurs for hydrogen 
C) is in the visible region 
D) involves the lowest possible quantum number n 
E) involves the highest possible quantum number n 
A) is the only one for which the Bohr theory can be used 
B) is the only series which occurs for hydrogen 
C) is in the visible region 
D) involves the lowest possible quantum number n 
E) involves the highest possible quantum number n

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 $\Psi$(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

The wave function for an electron in a state with zero angular momentum:

Accepted Answer

A) is zero everywhere 
B) is spherically symmetric 
C) depends on the angle from the z axis 
D) depends on the angle from the x axis 
E) is spherically symmetric for some shells and depends on the angle from the z axis for others 
A) is zero everywhere 
B) is spherically symmetric 
C) depends on the angle from the z axis 
D) depends on the angle from the x axis 
E) is spherically symmetric for some shells and depends on the angle from the z axis for others

Question 7

The quantum number n is most closely associated with what property of the electron in a hydrogen atom?

Accepted Answer

A) Energy 
B) Orbital angular momentum 
C) Spin angular momentum 
D) Magnetic moment 
E) z component of angular momentum 
A) Energy 
B) Orbital angular momentum 
C) Spin angular momentum 
D) Magnetic moment 
E) z component of angular momentum

Question 8

The binding energy of an electron in the ground state in a hydrogen atom is about:

Accepted Answer

A) 1.0 eV 
B) 3.4 eV 
C) 10.2 eV 
D) 13.6 eV 
E) 27.2 eV 
A) 1.0 eV 
B) 3.4 eV 
C) 10.2 eV 
D) 13.6 eV 
E) 27.2 eV

Question 9

The figure shows the energy levels for an electron in a finite potential energy well.If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon?

Accepted Answer

A) 6.0 nm 
B) 5.7 nm 
C) 5.3 nm 
D) 3.0 nm 
E) 2.3 nm 
A) 6.0 nm 
B) 5.7 nm 
C) 5.3 nm 
D) 3.0 nm 
E) 2.3 nm

Question 10

Two one-dimensional traps have infinite potential energy at their walls.Trap A has width L and trap B has width 2L.For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?

Accepted Answer

A) n = 1 
B) n = 2 
C) n = 3 
D) n = 4 
E) n = 5 
A) n = 1 
B) n = 2 
C) n = 3 
D) n = 4 
E) n = 5

Question 11

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

Accepted Answer

A) "4 $\pi$r2$\Psi$" 
B) "$\vert$$\Psi$$\vert$2" 
C) "4 $\pi$r2$\vert$$\Psi$$\vert$2" 
D) "4 $\pi$$\vert$$\Psi$$\vert$2" 
E) "4 $\pi$r$\vert$$\Psi$$\vert$2" 
A) "4 $\pi$r2$\Psi$" 
B) "$\vert$$\Psi$$\vert$2" 
C) "4 $\pi$r2$\vert$$\Psi$$\vert$2" 
D) "4 $\pi$$\vert$$\Psi$$\vert$2" 
E) "4 $\pi$r$\vert$$\Psi$$\vert$2"

Question 12

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 13

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 probability density P(x)versus x is shown.The value of the quantum number n is:

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 3 
E) 4 
A) 0 
B) 1 
C) 2 
D) 3 
E) 4

Question 14

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

Question 15

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then the ground state energy of a hydrogen atom is -13.6 eV.When the electron is in the first excited state its excitation energy (the difference between the energy of the state and that of the ground state)is:

Accepted Answer

A) 0 
B) 3.4 eV 
C) 6.8 eV 
D) 10.2 eV 
E) 13.6 eV 
A) 0 
B) 3.4 eV 
C) 6.8 eV 
D) 10.2 eV 
E) 13.6 eV

Question 16

When a hydrogen atom makes the transition from the second excited state to the ground state (at -13.6 eV)the energy of the photon emitted is:

Accepted Answer

A) 0 eV 
B) 1.5 eV 
C) 9.1 eV 
D) 12.1 eV 
E) 13.6 eV 
A) 0 eV 
B) 1.5 eV 
C) 9.1 eV 
D) 12.1 eV 
E) 13.6 eV

Question 17

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then, according to the quantum theory the energy En of a state with principal quantum number n is proportional to:

Accepted Answer

A) n 
B) n2 
C) 1/n 
D) 1/n2 
E) none of the above 
A) n 
B) n2 
C) 1/n 
D) 1/n2 
E) none of the above

Question 18

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 19

An electron in an atom drops from an energy level at -1.1 *10-18 J to an energy level at -2.4 * 10-18 J.The wave associated with the emitted photon has a frequency of:

Accepted Answer

A) 2.0 * 1017 Hz 
B) 2.0 *1015 Hz 
C) 2.0 * 1013 Hz 
D) 2.0 *1011 Hz 
E) 2.0 * 109 Hz 
A) 2.0 * 1017 Hz 
B) 2.0 *1015 Hz 
C) 2.0 * 1013 Hz 
D) 2.0 *1011 Hz 
E) 2.0 * 109 Hz

Question 20

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) P dr 
B) "$\vert$P $\vert$2 dr 
C) "4 $\pi$r2P dr" 
D) "4 $\pi$r2$\vert$P $\vert$ dr" 
E) "4 $\pi$$\vert$P $\vert$ dr" 
A) P dr 
B) "$\vert$P $\vert$2 dr 
C) "4 $\pi$r2P dr" 
D) "4 $\pi$r2$\vert$P $\vert$ dr" 
E) "4 $\pi$$\vert$P $\vert$ dr"

Exam 39: More About Matter Waves

An electron confined in a one-dimensional infinite potential well has an energy of 180 eV.What is its wavelength?

An electron is trapped in a deep well with a width of 0.3 nm.If it is in the state with quantum number n = 3 its kinetic energy is:

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many nodes does the probability density have (counting the nodes at the ends of the well)?

The Balmer series of hydrogen is important because it:

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 Ψ\PsiΨ (x)versus x is shown.The value of quantum number n is:

The wave function for an electron in a state with zero angular momentum:

The quantum number n is most closely associated with what property of the electron in a hydrogen atom?

The binding energy of an electron in the ground state in a hydrogen atom is about:

The figure shows the energy levels for an electron in a finite potential energy well.If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon?

Two one-dimensional traps have infinite potential energy at their walls.Trap A has width L and trap B has width 2L.For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?

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

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 trap with zero potential energy in the interior and infinite potential energy at the walls.A graph of its probability density P(x)versus x is shown.The value of the quantum number n is:

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.

When a hydrogen atom makes the transition from the second excited state to the ground state (at -13.6 eV)the energy of the photon emitted is:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then, according to the quantum theory the energy En of a state with principal quantum number n is proportional to:

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?

An electron in an atom drops from an energy level at -1.1 *10-18 J to an energy level at -2.4 * 10-18 J.The wave associated with the emitted photon has a frequency of:

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:

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

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then, according to the quantum theory the energy E_n of a state with principal quantum number n is proportional to:

An electron in an atom drops from an energy level at -1.1 10^-18 J to an energy level at -2.4 10^-18 J.The wave associated with the emitted photon has a frequency of: