Deck 33: The Nature and Propagation of Light

Question 1

Molecular rotation: A rotating diatomic molecule in its l = 1 quantum state has energy E. What is the energy of the same molecule in its l = 2 quantum state?

A) 2E
B) 3E
C) 4E
D) 6E
E) 8E

Answer 1

3E

Question 2

Semiconductors: An unfilled electron state in the valence band is called

A) a hole.
B) an empty electron.
C) a conduction electron.
D) a positron.
E) an empty positron.

Answer 2

a hole.

Question 3

Molecular rotation: Estimate the rotational energy (in eV) for a diatomic hydrogen molecule in the l = 2 quantum state. (The equilibrium separation for the H₂ molecule is 0.074 nm.) (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, m_h ≈ m_proton = 1.67 × 10^-27 kg)

A) 0.011 eV
B) 0.026 eV
C) 0.032 eV
D) 0.046 eV
E) 0.055 eV

Answer 3

0.046 eV

Question 4

Molecular vibration: The vibrational frequency of an HF molecule is 8.72 × 10¹³ Hz and the reduced mass of the molecule is 1.589 × 10^-27 kg. What is the ground state vibrational energy of an HF molecule? (1 eV = 1.60 × 10^-19 J, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

A) 0.12 eV
B) 0.18 eV
C) 0.24 eV
D) 0.30 eV
E) 0.36 eV

Question 5

Molecular rotation: A rotating diatomic molecule has rotational quantum number l. The energy DIFFERENCE between adjacent energy levels

A) increases as l increases.
B) decreases as l increases.
C) is the same for all changes in l.
D) is independent of l.

Question 6

Molecular rotation: A diatomic molecule has 18 × 10^-5 eV of rotational energy in the l = 2 quantum state. What is its rotational energy in the l = 0 quantum state?

A) 90 µeV
B) 60 µeV
C) 30 µeV
D) 15 µeV
E) 0 eV

Question 7

Molecular vibration: A vibrating diatomic molecule has vibrational quantum number n. The energy DIFFERENCE between adjacent energy levels

A) increases as n increases.
B) decreases as n increases.
C) is the same for all changes in n.
D) is independent of n.

Question 8

Molecular rotation: The moment of inertia of a fluorine ( ) molecule is What is the rotational energy of a fluorine molecule for the l = 19 state? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 4.2 × 10^-2 eV
B) 2.1 × 10^-3 eV
C) 4.6 × 10^-2 eV
D) 5.1 × 10^-2 eV
E) 5.6 × 10^-2 eV

Question 9

Molecular rotation: A diatomic molecule has 2.6 × 10^-5 eV of rotational energy in the l = 2 quantum state. What is its rotational energy in the l = 1 quantum state?

A) 3.4 µeV
B) 4.1 µeV
C) 5.3 µeV
D) 7.8 µeV
E) 8.7 µeV

Question 10

Molecular bonds: Covalent bonding is due to

A) the sharing of electrons between atoms.
B) the transfer of electrons between atoms.
C) atoms bonding to hydrogen molecules.
D) atoms bonding to oxygen molecules.

Question 11

Molecular rotation: A certain molecule has 2.00 eV of rotational energy in the l = 1 state. In the l = 4 state, what would its rotational energy be?

A) 8.00 eV
B) 16.0 eV
C) 20.0 eV
D) 30.0 eV
E) 32.0 eV

Question 12

Molecular rotation: A diatomic molecule has a moment of inertia of 7.73 × 10^-45 kg∙ m². What is its rotational energy in the quantum state characterized by l = 2? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 22.7 µeV
B) 27.0 µeV
C) 587 µeV
D) 72.2 µeV
E) 87.1 µeV

Question 13

Molecular rotation: The spacing of the atoms (treated as point masses) in the H₂ molecule is 7.4 × 10^-11 m. What is the energy of the l = 1 rotational level? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, m_h ≈ m_proton = 1.67 × 10^-27 kg)

A) 0.090 eV
B) 0.070 eV
C) 0.045 eV
D) 0.030 eV
E) 0.015 eV

Question 14

Molecular rotation: When a certain diatomic molecule undergoes a transition from the l = 5 to the l = 3 rotational level, the emitted photon has wavelength Calculate the moment of inertia of the molecule. (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s)

Question 15

Molecular bonds: Ionic bonding is due to

A) the sharing of electrons between atoms.
B) the transfer of electrons between atoms.
C) atoms bonding to hydrogen molecules.
D) atoms bonding to oxygen molecules.

Question 16

Semiconductors: In a p-type semiconductor, a hole is

A) a donor atom.
B) an extra electron supplied by a donor atom.
C) an extra proton supplied by a donor atom.
D) a missing atom in the crystalline structure.
E) a region where an electron is missing.

Question 17

Molecular vibration: A vibrating diatomic molecule in its ground state has energy E. What is the energy of the same molecule in its second EXCITED state?

A) E
B) 2E
C) 3E
D) 5E
E) 9E

Question 18

Molecular vibration: A certain diatomic molecule emits a photon of energy 1.20 eV when it makes a transition from the n = 1 vibrational state to the next lower vibrational state. What is the frequency of vibration of the molecule? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 1.93 × 10¹⁴ Hz
B) 2.90 × 10¹⁴ Hz
C) 4.35 × 10¹⁴ Hz
D) 1.82 × 10¹⁵ Hz
E) 2.73 × 10¹⁵ Hz

Question 19

Molecular vibration: A diatomic molecule is vibrating in its first excited quantum state above the ground state. In that excited state, its frequency is 2.0 × 10¹³ Hz. What is the energy of the molecule in this state? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J

A) 0.041 eV
B) 0.083 eV
C) 0.12 eV
D) 0.15 eV
E) 0.17 eV

Question 20

Semiconductors: A p-type semiconductor has a net positive charge.

Question 21

Molecular vibration: A certain diatomic molecule emits a photon of energy 1.20 eV when it makes a transition from the n = 1 vibrational state to the next lower vibrational state. If the molecule made a transition from the n = 2 state to the n = 1 state, what would be the energy of the photon it would emit? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 3.60 eV
B) 2.40 eV
C) 1.20 eV
D) 0.60 eV
E) 0.30 eV

Question 22

Free-electron theory of metals: The Fermi energy of rubidium at a temperature of 5 K is 1.85 eV. An electron state in rubidium is 0.007 eV above the Fermi level. What is the probability that this state is occupied at a temperature of 9K? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, Boltzmann constant = 1.38 ∙ 10^-23 J/K, 1 eV = 1.60 × 10^-19 J)

A) 1 × 10^-4
B) 2 × 10^-5
C) 5 × 10^-6
D) 1 × 10^-6
E) 2 × 10^-7

Question 23

Semiconductors: The energy gap between the valence and conduction bands in a certain semiconductor is 1.25 eV. What is the threshold wavelength for optical absorption in this substance? (c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A) 599 nm
B) 639 nm
C) 959 nm
D) 873 nm
E) 994 nm

Question 24

Free-electron theory of metals: If a metal had a Fermi level (energy) of 5.0 eV, what would be the average energy of the electrons at 0 K?

A) 8.0 eV
B) 6.0 eV
C) 3.0 eV
D) 0.00 eV
E) 5.0 eV

Question 25

Free-electron theory of metals: If one metal has double the number of conduction electrons per unit volume of a second metal, then its Fermi level (energy) is how many times that of the second metal?

A) 1.41
B) 2.83
C) 2.00
D) 3.22
E) 1.59

Question 26

Free-electron theory of metals: A metal has a Fermi level (energy) of 5.50 eV. At 1200 K, what energy will have a 90% occupancy probability? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, Boltzmann constant = 1.38 × 10^-23, 1 eV = 1.60 × 10^-19 J)

A) 5.79 eV
B) 5.73 eV
C) 5.56 eV
D) 5.44 eV
E) 5.27 eV

Question 27

Free-electron theory of metals: For a solid in which the occupation of the energy states is given by the Fermi-Dirac distribution, the probability that a certain state is occupied at a temperature T₀ is 0.70. If the temperature is doubled to 2T₀, what is the probability that the same state is occupied? Assume that the Fermi energy does not change with temperature.

Question 28

Free-electron theory of metals: Silver has a Fermi level (energy) of 5.5 eV. At 0 K, at what speed would the electrons be moving if they had kinetic energy equal to the Fermi energy? (This speed is known as the Fermi speed.) (m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A) 1400 km/s
B) 1.0 km/s
C) 2.2 km/s
D) 1100 km/s
E) 3.5 km/s

Question 29

Free-electron theory of metals: What is the occupancy probability at an energy of 12.00 eV for a material with a Fermi energy (level) of 11.63 eV at a temperature of 500 K? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, Boltzmann constant = 1.38 × 10^-23, 1 eV = 1.60 × 10^-19 J)

A) 0.00030%
B) 0.019%
C) 2.0%
D) 6.0%
E) 12%

Question 30

Free-electron theory of metals: The Fermi level (energy) of a metal is 5.5 eV. What is the number of conduction electrons per unit volume for this metal? (m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A) 5.8 × 10²⁸ / m³
B) 6.2 × 10²⁸ / m³
C) 4.1 × 10²⁸ / m³
D) 8.4 × 10²⁸ / m³
E) 3.3 × 10²⁸ / m³

Question 31

Density of states: Approximately how many states in the range from 5.0 eV to 5.2 eV are there in a copper bar of volume 5.3 cm³? (h = 6.626 × 10^-34 J ∙ s, ħ = 1.055 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 5.1 × 10²²
B) 3.2 × 10²²
C) 1.6 × 10²²
D) 8.2 × 10²¹
E) 3.2 × 10²¹