Question 1

The energy of a molecule can normally be divided into the following categories:

Accepted Answer

A)  rotational and vibrational 
B)  translational, rotational and vibrational 
C)  electronic, translational, rotational, and vibrational 
D)  rotational 
E)  electronic 
A)  rotational and vibrational 
B)  translational, rotational and vibrational 
C)  electronic, translational, rotational, and vibrational 
D)  rotational 
E)  electronic

Question 2

The dissociation energy of the hydrogen molecule is approximately 5 eV. What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV?

Accepted Answer

A)  28990 K 
B)  57970 K 
C)  38650 K 
D)  23190 K 
E)  12880 K 
A)  28990 K 
B)  57970 K 
C)  38650 K 
D)  23190 K 
E)  12880 K

Question 3

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1, the change in energy, EJ + 1 − EJ, is

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  . 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  .

Question 4

An oxygen molecule has a moment of inertia of 5 × 10−46 kg ⋅ m2. Calculate the bond length (in nm). Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−27 kg).

Accepted Answer

A)  0.3 
B)  0.1 
C)  0.2 
D)  0.4 
E)  0.5 
A)  0.3 
B)  0.1 
C)  0.2 
D)  0.4 
E)  0.5

Question 5

The Fermi energy of a metal at a temperature T is 7.0 eV. What is the average energy (in eV) of a conduction electron at that temperature?

Accepted Answer

A)  2.8 
B)  7.0 
C)  3.5 
D)  4.2 
E)  4.7 
A)  2.8 
B)  7.0 
C)  3.5 
D)  4.2 
E)  4.7

Question 6

In comparing vibrational and rotational levels in molecules, we find that the energy separation between adjacent energy levels is

Accepted Answer

A)  the same in rotational and vibrational levels. 
B)  greater in rotational than in vibrational levels. 
C)  greater in vibrational than in rotational levels. 
D)  directly proportional with one rotational level for each vibrational level. 
E)  inversely proportional with one rotational level for each vibrational level. 
A)  the same in rotational and vibrational levels. 
B)  greater in rotational than in vibrational levels. 
C)  greater in vibrational than in rotational levels. 
D)  directly proportional with one rotational level for each vibrational level. 
E)  inversely proportional with one rotational level for each vibrational level.

Question 7

An LED emits light of wavelength 600 nm. What is its band gap?

Accepted Answer

A)  1.11 eV 
B)  1.54 eV 
C)  1.99 eV 
D)  2.07 eV 
E)  2.33 eV 
A)  1.11 eV 
B)  1.54 eV 
C)  1.99 eV 
D)  2.07 eV 
E)  2.33 eV

Question 8

The rotation spectrum of the HCl molecule has been observed in the far infrared, around 50 × 10−6 m. The spacing between successive lines in the spectrum corresponds to radiation of wavelength equal to 5 microns (1 μm = 10−6 m). Determine the frequency of the photon associated with this transition.

Accepted Answer

A)  6 × 1014 Hz 
B)  6 × 1012 Hz 
C)  6 × 1011 Hz 
D)  6 × 1013 Hz 
E)  6 × 1010 Hz 
A)  6 × 1014 Hz 
B)  6 × 1012 Hz 
C)  6 × 1011 Hz 
D)  6 × 1013 Hz 
E)  6 × 1010 Hz

Question 9

How many degrees of freedom does a diatomic molecule have?

Accepted Answer

A)  3 
B)  6 
C)  5 
D)  7 
E)  9 
A)  3 
B)  6 
C)  5 
D)  7 
E)  9

Question 10

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 1011 Hz. The moment of inertia of the molecule (in kg ⋅ m2) is

Accepted Answer

A)  5.70 × 10−45 
B)  1.45 × 10−46 
C)  1.12 × 10−44 
D)  2.91 × 10−46 
E)  9.11 × 10−46 
A)  5.70 × 10−45 
B)  1.45 × 10−46 
C)  1.12 × 10−44 
D)  2.91 × 10−46 
E)  9.11 × 10−46

Question 11

In the Lennard-Jones model of the hydrogen molecule, the potential is given by   . In this model, the minimum internuclear separation, r0, is

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  . 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  .

Question 12

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by

Accepted Answer

A)  the probability that a state is unoccupied,
  . 
B)  the probability that a state is occupied,
  . 
C)  the probability that a state is unoccupied,
  . 
D)  the probability that a state is occupied,
  . 
E)  dE alone. 
A)  the probability that a state is unoccupied,
  . 
B)  the probability that a state is occupied,
  . 
C)  the probability that a state is unoccupied,
  . 
D)  the probability that a state is occupied,
  . 
E)  dE alone.

Question 13

The fundamental frequency of HF is 8.72 × 1013 Hz. The energy associated with a transition from the 10th to the 9th vibrational quantum number (in eV) is

Accepted Answer

A)  3.61 
B)  0.361 
C)  0.060 5 
D)  0.605 
E)  0.182 
A)  3.61 
B)  0.361 
C)  0.060 5 
D)  0.605 
E)  0.182

Question 14

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−9 m). How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm3.

Accepted Answer

Question 15

Because HF, hydrogen fluoride, is a covalent gaseous molecule at room temperature, we might reasonably expect that at room temperature HCl, hydrogen chloride, is

Accepted Answer

A)  a covalent gaseous molecule. 
B)  a covalent solid. 
C)  a metallic gas. 
D)  a metallic solid. 
E)  an ionic solid. 
A)  a covalent gaseous molecule. 
B)  a covalent solid. 
C)  a metallic gas. 
D)  a metallic solid. 
E)  an ionic solid.

Question 16

The Fermi energy corresponds to

Accepted Answer

A)  the maximum energy electrons can have in a metal at T = 0 K. 
B)  the maximum energy electrons can have in a metal at T = 0 C. 
C)  the minimum energy electrons can have in a metal at T = 0 K. 
D)  the number of electrons per unit volume between E and E + dE. 
E)  the minimum energy electrons can have in a metal at T = 0 C. 
A)  the maximum energy electrons can have in a metal at T = 0 K. 
B)  the maximum energy electrons can have in a metal at T = 0 C. 
C)  the minimum energy electrons can have in a metal at T = 0 K. 
D)  the number of electrons per unit volume between E and E + dE. 
E)  the minimum energy electrons can have in a metal at T = 0 C.

Question 17

When a voltage ΔV is applied to a p-n junction diode at absolute temperature T, the current voltage relationship is

Accepted Answer

A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  . 
A) 
  . 
B) 
  . 
C) 
  . 
D) 
  . 
E) 
  .

Question 18

Solid argon has a density of 1650 kg/m3. The atomic weight of argon is 40.0. Assuming each atom occupies a cubical volume, what is the distance between the argon atoms?

Accepted Answer

Question 19

The Fermi temperature of copper is 80 000 K. The corresponding Fermi energy (in eV) is

Accepted Answer

A)  7 
B)  5 
C)  3 
D)  1 
E)  4 
A)  7 
B)  5 
C)  3 
D)  1 
E)  4

Question 20

Ellis and Randy are looking at a molecular absorption spectrum. The spectral lines appear to fall into two groups with a gap in the middle. Ellis says that this must be an absorption spectrum for transitions between the v = 0 and v = 1 vibrational states of a diatomic molecule. Randy says the gap in the middle must occur because a ΔJ = 0 transition is forbidden. Which one, if either, is correct, and why?

Accepted Answer

A)  Ellis, because rotational levels are separated by greater energy differences than vibrational levels. 
B)  Randy, because rotational levels are separated by greater energy differences than vibrational levels. 
C)  Ellis, because the ΔJ = 0 transition is the most prominent spectral line in transitions between vibrational levels. 
D)  Neither, because rotational levels are separated by greater energies that vibrational levels and ΔJ = 0 transitions are not forbidden. 
E)  Both, because vibrational levels are separated by greater energy differences than rotational levels and ΔJ = 0 transitions are forbidden. 
A)  Ellis, because rotational levels are separated by greater energy differences than vibrational levels. 
B)  Randy, because rotational levels are separated by greater energy differences than vibrational levels. 
C)  Ellis, because the ΔJ = 0 transition is the most prominent spectral line in transitions between vibrational levels. 
D)  Neither, because rotational levels are separated by greater energies that vibrational levels and ΔJ = 0 transitions are not forbidden. 
E)  Both, because vibrational levels are separated by greater energy differences than rotational levels and ΔJ = 0 transitions are forbidden.

Exam 43: Molecules and Solids

The energy of a molecule can normally be divided into the following categories:

The dissociation energy of the hydrogen molecule is approximately 5 eV. What is the temperature of a monatomic molecule whose kinetic energy is equal to 5.000 eV?

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1, the change in energy, EJ + 1 − EJ, is

An oxygen molecule has a moment of inertia of 5 × 10−46 kg ⋅ m2. Calculate the bond length (in nm). Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−27 kg).

The Fermi energy of a metal at a temperature T is 7.0 eV. What is the average energy (in eV) of a conduction electron at that temperature?

In comparing vibrational and rotational levels in molecules, we find that the energy separation between adjacent energy levels is

An LED emits light of wavelength 600 nm. What is its band gap?

How many degrees of freedom does a diatomic molecule have?

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 1011 Hz. The moment of inertia of the molecule (in kg ⋅ m2) is

In the Lennard-Jones model of the hydrogen molecule, the potential is given by . In this model, the minimum internuclear separation, r0, is

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by

The fundamental frequency of HF is 8.72 × 1013 Hz. The energy associated with a transition from the 10th to the 9th vibrational quantum number (in eV) is

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−9 m). How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm3.

Because HF, hydrogen fluoride, is a covalent gaseous molecule at room temperature, we might reasonably expect that at room temperature HCl, hydrogen chloride, is

The Fermi energy corresponds to

When a voltage ΔV is applied to a p-n junction diode at absolute temperature T, the current voltage relationship is

Solid argon has a density of 1650 kg/m3. The atomic weight of argon is 40.0. Assuming each atom occupies a cubical volume, what is the distance between the argon atoms?

The Fermi temperature of copper is 80 000 K. The corresponding Fermi energy (in eV) is

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When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1, the change in energy, EJ_{+ 1} − E_J, is

An oxygen molecule has a moment of inertia of 5 × 10−⁴⁶ kg ⋅ m². Calculate the bond length (in nm). Recall that the atomic mass of oxygen is 16 u (1 u = 1.66 × 10−²⁷ kg).

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 10¹¹ Hz. The moment of inertia of the molecule (in kg ⋅ m²) is

In the Lennard-Jones model of the hydrogen molecule, the potential is given by . In this model, the minimum internuclear separation, r₀, is

The fundamental frequency of HF is 8.72 × 10¹³ Hz. The energy associated with a transition from the 10th to the 9th vibrational quantum number (in eV) is

The smallest object one can distinguish using the electron microscope is on the order of one nanometer (1 nm = 10−⁹ m). How many atoms of gold are contained in a cube whose edge is 1 nm long? The atomic mass of gold is 197 and its density is 19.3 g/cm³.

Solid argon has a density of 1650 kg/m³. The atomic weight of argon is 40.0. Assuming each atom occupies a cubical volume, what is the distance between the argon atoms?