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)  none 
B)  7 
C)  13 
D)  14 
E)  15 
A)  none 
B)  7 
C)  13 
D)  14 
E)  15 D

Question 2

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 D

Question 3

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:

Accepted Answer

A)  the kinetic energy is negative 
B)  the potential energy is positive 
C)  the electron might escape from the atom 
D)  the electron and proton are bound together 
E)  none of the above 
A)  the kinetic energy is negative 
B)  the potential energy is positive 
C)  the electron might escape from the atom 
D)  the electron and proton are bound together 
E)  none of the above D

Question 4

The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
E)  V 
A)  I 
B)  II 
C)  III 
D)  IV 
E)  V

Question 5

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 6

The principle of complementarity is due to:

Accepted Answer

A)  Einstein 
B)  Maxwell 
C)  Newton 
D)  Bohr 
E)  Schrodinger 
A)  Einstein 
B)  Maxwell 
C)  Newton 
D)  Bohr 
E)  Schrodinger

Question 7

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

Accepted Answer

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

Question 8

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 9

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. 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 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 10

Take the potential energy of a hydrogen atom to be zero for infinite seperation 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 11

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

Question 12

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 13

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 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

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)  4 
D)  6 
E)  8 
A)  0 
B)  1 
C)  4 
D)  6 
E)  8

Question 16

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 17

The radial probability density for the electron in the ground state of a hydrogen atom has a peak at about:

Accepted Answer

A)  0.5 pm 
B)  5 pm 
C)  50 pm 
D)  500 pm 
E)  5000 pm 
A)  0.5 pm 
B)  5 pm 
C)  50 pm 
D)  500 pm 
E)  5000 pm

Question 18

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)  none 
B)  7 
C)  13 
D)  14 
E)  15 
A)  none 
B)  7 
C)  13 
D)  14 
E)  15

Question 19

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

Accepted Answer

A)  $\int$$\mid$$\Psi$$\mid$2dt = 1 
B)  $\int$$\mid$ $\Psi$$\mid$2dx = 1 
C)  $\partial$ $\Psi$/$\partial$ x = 1 
D)  $\partial$ $\Psi$/$\partial$ t = 1 
E)  $\mid$$\Psi$$\mid$2 = 1 
A)  $\int$$\mid$$\Psi$$\mid$2dt = 1 
B)  $\int$$\mid$ $\Psi$$\mid$2dx = 1 
C)  $\partial$ $\Psi$/$\partial$ x = 1 
D)  $\partial$ $\Psi$/$\partial$ t = 1 
E)  $\mid$$\Psi$$\mid$2 = 1

Question 20

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

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?

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:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:

The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?

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 principle of complementarity is due to:

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

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:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. 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 is:

Take the potential energy of a hydrogen atom to be zero for infinite seperation 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:

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):

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

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:

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?

The radial probability density for the electron in the ground state of a hydrogen atom has a peak at about:

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)?

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

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

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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 seperation 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 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:

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