# Worksheet: Molecular Energy Levels

In this worksheet, we will practice calculating molecular rotational and vibrational energies, atomic equilibrium separations, and dissociation energies.

**Q6: **

An H_{2} molecule with an equilibrium separation distance of 0.0750 nm can have various rotational energy states.

Determine the rotational energy of the state. Given the mass of Hydrogen kg

Determine the rotational energy of the state.

- A eV
- B eV
- C eV
- D eV
- E eV

Determine the rotational energy of the state.

- A eV
- B eV
- C eV
- D eV
- E eV

**Q10: **

Molecular hydrogen is kept at a temperature of 300 K in a cubical container with sides each 15.0 cm long. Consider the molecules as though they are moving in a one-dimensional box. Take the mass of one mole of hydrogen to be 2.01588 g.

Find the ground state energy of a hydrogen molecule in the container.

- A J
- B J
- C J
- D J
- E J

Assume that a molecule has a thermal energy given by and find the corresponding quantum number of the quantum state to this thermal energy.

- A
- B
- C
- D
- E

**Q11: **

Vibrations of an molecule can be modeled as a simple harmonic oscillator with the spring constant , and the mass of the hydrogen atom is . The molecule makes a transition between its third and second excited states.

What is the vibrational frequency of this molecule before it makes the transition?

- A
- B
- C
- D
- E

What is the energy of the photon emitted during the transition?

- A
- B
- C
- D
- E

What is the wavelength of the photon emitted during the transition?

- A14.3 μm
- B2.27 μm
- C1.60 μm
- D0.256 μm
- E10.0 μm

**Q12: **

A diatomic molecule behaves like a quantum harmonic oscillator with the force constant 15.0 N/m and mass kg. The molecule makes the transition from the third excited state to the second excited state, during which it emits a photon.

What is the wavelength of the photon?

- A m
- B m
- C m
- D m
- E m

Find the ground state energy of vibrations for this molecule.

- A J
- B J
- C J
- D J
- E J

**Q13: **

In a physics lab, you measure the vibrational–rotational spectrum of potassium bromide (KBr). The estimated separation between the lowest absorption peaks Hz, and the central frequency of the band Hz.

What is the moment of inertia of a KBr molecule?

- A kg⋅m
^{2} - B kg⋅m
^{2} - C kg⋅m
^{2} - D kg⋅m
^{2} - E kg⋅m
^{2}

What is the energy of vibration of a KBr molecule of the lowest energy level?

- A J
- B J
- C J
- D J
- E J

**Q14: **

The vibrational–rotational spectrum of HCl is measured in a lab. The estimated separation between absorption peaks . The central frequency of the band .

What is the moment of inertia of an HCl molecule?

- A kg⋅m
^{2} - B kg⋅m
^{2} - C kg⋅m
^{2} - D kg⋅m
^{2} - E kg⋅m
^{2}

What is the energy of vibration of an HCl molecule of the lowest energy level?

- A J
- B J
- C J
- D J
- E J

**Q15: **

Transitions in the rotational energy spectrum of a molecule are observed at a temperature of 300 K. If a peak in the spectrum corresponds to a transition from the state to the state, what is the moment of inertia of the molecule? Answer to one significant figure.

- A kg⋅m
^{2} - B kg⋅m
^{2} - C kg⋅m
^{2} - D kg⋅m
^{2} - E kg⋅m
^{2}