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

Accepted Answer

The energy of a rotating diatomic molecule is given by E_l = l(l+1)ħ²/2I, where l is the quantum number. For l = 1, E_1 = 2ħ²/2I = ħ²/I. For l = 2, E_2 = 6ħ²/2I = 3ħ²/I. Therefore, E_2 = 3E_1, so the energy is 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.

Accepted Answer

An unfilled electron state in the valence band is called a hole in semiconductors.

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

Accepted Answer

D

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

Accepted Answer

The ground state vibrational energy (E) of a molecule can be calculated using the formula $E = \frac{1}{2}h\nu$, where $h$ is Planck's constant and $\nu$ is the vibrational frequency. Given $h = 6.626 \times 10^{-34}$ J·s and $\nu = 8.72 \times 10^{13}$ Hz, $E = \frac{1}{2} \times 6.626 \times 10^{-34} \times 8.72 \times 10^{13} = 2.89 \times 10^{-20}$ J. Converting to eV using $1 \text{ eV} = 1.60 \times 10^{-19}$ J, $E = \frac{2.89 \times 10^{-20}}{1.60 \times 10^{-19}} = 0.18$ 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.

Accepted Answer

The energy difference between adjacent energy levels in a rotating diatomic molecule increases as the rotational quantum number $l$ increases. This is because the energy levels are quantized and the spacing between them is proportional to $l(l+1)$, making the energy difference larger for higher values 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

Accepted Answer

The rotational energy levels of a diatomic molecule are quantized and given by the formula $E_l = \frac{h^2}{8\pi^2I}l(l+1)$, where $E_l$ is the energy of the level with quantum number $l$, $h$ is Planck's constant, and $I$ is the moment of inertia of the molecule. For $l = 0$, the formula gives $E_0 = 0$ because $l(l+1) = 0$, indicating that there is no rotational energy in the $l = 0$ quantum state.

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.

Accepted Answer

The answer of Molecular vibration: A vibrating diatomic molecule has...

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

Accepted Answer

The answer of Molecular rotation: The moment of inertia of...

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

Accepted Answer

The rotational energy levels of a diatomic molecule are given by $E_l = \frac{h^2}{8\pi^2I}l(l+1)$, where $E_l$ is the energy of the level with quantum number $l$, $h$ is Planck's constant, and $I$ is the moment of inertia of the molecule. The energy difference between levels depends on $l$, so the energy for $l = 1$ can be calculated relative to $l = 2$ given the energy for $l = 2$.Given $E_{l=2} = 2.6 \times 10^{-5}$ eV, to find $E_{l=1}$, we use the ratio of the $l(l+1)$ terms because the rest of the formula (constants and $I$) remains the same for both states. For $l = 2$, $l(l+1) = 2 \times 3 = 6$, and for $l = 1$, $l(l+1) = 1 \times 2 = 2$.The energy for $l = 1$ is thus $\frac{2}{6}$ of the energy for $l = 2$, or $E_{l=1} = \frac{2}{6} \times 2.6 \times 10^{-5}$ eV. This calculation simplifies to $E_{l=1} = \frac{1}{3} \times 2.6 \times 10^{-5}$ eV = $0.866 \times 10^{-5}$ eV, or $8.7 \times 10^{-6}$ eV, which is 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.

Accepted Answer

Covalent bonding is a type of chemical bond in which atoms share electrons with each other to form a stable molecule. The sharing of electrons between atoms forms the covalent bond, which holds the atoms together. Transfer of electrons between atoms (option B) is seen in ionic bonding, not covalent bonding. Options C and D refer to specific examples of covalent bonding but do not encompass all the possibilities.

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

Accepted Answer

The answer of Molecular rotation: A certain molecule has 2.00...

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

Accepted Answer

The answer of Molecular rotation: A diatomic molecule has a...

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

Accepted Answer

The energy of a rotational level is given by E = l(l+1)ħ²/(2I), where I is the moment of inertia I = μr², and μ is the reduced mass μ = m_h/2 for H₂. Substituting the values, E = 1(1+1)(1.055×10⁻³⁴)²/(2×(1.67×10⁻²⁷/2)×(7.4×10⁻¹¹)²) ≈ 2.4×10⁻²¹ J = 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)

Accepted Answer

The answer of Molecular rotation: When a certain diatomic molecule...

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.

Accepted Answer

Ionic bonding occurs when one or more electrons are transferred from one atom to another, resulting in the formation of positively and negatively charged ions that are held together by electrostatic attraction.

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.

Accepted Answer

In a p-type semiconductor, a hole is a region where an electron is missing. This occurs due to the doping of the semiconductor with impurity atoms that have one less valence electron than the host semiconductor atoms, creating a shortage of electrons and thus a deficiency or "hole" in the valence band. These holes can act as positive charge carriers in the semiconductor.

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

Accepted Answer

The energy levels of a vibrating diatomic molecule are quantized and given by the formula E_n = (n + 1/2)hv, where n is the quantum number (starting from 0 for the ground state). The ground state (n=0) has energy E = (1/2)hv. The second excited state corresponds to n=2, which gives E_2 = (2 + 1/2)hv = (5/2)hv. Since the ground state energy E = (1/2)hv, the energy of the second excited state is 5 times the ground state energy, or 5E.

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

Accepted Answer

First, we need to find the energy difference between the two vibrational levels:

ΔE = E(n=1) - E(n=0) = 1.20 eV

We can convert this to joules:

ΔE = (1.20 eV)(1.60 × 10^-19 J/eV) = 1.92 × 10^-19 J

Since energy is related to frequency and Planck's constant by the equation:

E = hν

We can rearrange this to solve for frequency:

ν = E/h

Plugging in the values we have:

ν = (1.92 × 10^-19 J)/(6.626 × 10^-34 J∙s)

ν = 2.90 × 10^14 Hz

This matches choice B, so the answer is B.

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

Accepted Answer

The answer of Molecular vibration: A diatomic molecule is vibrating...

Question 20

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

Accepted Answer

A p-type semiconductor is electrically neutral overall; it has more holes (positive charge carriers) than electrons, but the material as a whole remains neutral because the number of protons in the semiconductor's nuclei balances out the total charge.

Quiz 33: The Nature and Propagation of Light

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?

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

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, mh ≈ mproton = 1.67 × 10-27 kg)

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)

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

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?

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

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)

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?

Molecular bonds: Covalent bonding is due to

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?

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)

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, mh ≈ mproton = 1.67 × 10-27 kg)

Molecular bonds: Ionic bonding is due to

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

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?

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

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

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)

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?

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)

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?

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)

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)