Deck 39: More About Matter Waves

Question 1

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:

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

Answer 1

2.0* 10¹⁵ Hz

Question 2

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.

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

Answer 2

2, 3, 1

Question 3

A particle is confined by finite potential energy walls to a one-dimensional trap from x = 0 to x = L. Its wave function in the region x > L has the form:

A) $\Psi$ (x) = A sin(kx)
B) $\Psi$ (x) = Ae^kx
C) $\Psi$ (x) = Ae^-kx
D) $\Psi$ (x) = Ae^ikx
E) $\Psi$ (x) = 0

Answer 3

$\Psi$ (x) = Ae^-kx

Question 4

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

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 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:

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

An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:

A) 5.4 * 10 ^{- 7} m
B) 3.0 *10 ^{- 7} m
C) 1.7 * 10 ^{- 7} m
D) 1.2 *10 ^{- 7} m
E) 1.0 *10 ^{- 7} m

Question 7

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)?

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

Question 8

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

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 9

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) 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

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?

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

Question 11

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?

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

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:

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

Question 13

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:

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

Question 14

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

Question 15

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.

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 16

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.

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 17

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

A) 65 pm
B) 91 pm
C) 130 pm
D) 370 pm
E) 520 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 maxima does the probability density have?

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

Question 19

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:

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

Question 20

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:

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

Question 21

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

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

Question 22

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?

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

Question 23

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:

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

Question 24

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

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 25

The Balmer series of hydrogen is important because it:

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 26

Which of the following sets of quantum numbers is possible for an electron in a hydrogen atom?

A) n = 4, ℓ = 3, m_ℓ = −3
B) n = 4, ℓ = 4, m_ℓ = −2
C) n = 5, ℓ = −1, m_ℓ = 2
D) n = 3, ℓ = 1, m_ℓ = −2
E) n = 2, ℓ = 3, m_ℓ = −2

Question 27

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

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

Question 28

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

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 29

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

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

Question 30

Consider the following: Of these which are spherically symmetric?

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

Question 31

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

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

Question 32

A particle is trapped in a finite potential energy well that is deep enough so that the electron can be in the state with n = 4. For this state how many nodes does the probability density have?

A) 0
B) 1
C) 3
D) 4
E) 5

Question 33

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. The energy of the first excited state is:

A) 0 eV
B) -3.4 eV
C) -6.8 eV
D) -10.2 eV
E) -27 eV

Question 34

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?

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 35

A particle in a certain finite potential energy well can have any of five quantized energy values and no more. Which of the following would allow it to have any of six quantized energy levels?

A) Increase the momentum of the particle
B) Decrease the momentum of the particle
C) Decrease the well width
D) Increase the well depth
E) Decrease the well depth

Question 36

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?

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

Question 37

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:

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

Question 38

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. The minus sign indicates:

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

Question 39

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:

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

Question 40

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:

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

Question 41

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

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