# Worksheet: Molecular Energy Levels

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

Q1:

The characteristic energy of the N2 molecule is eV. Determine the separation distance between the nitrogen atoms.

Q2:

Find the equilibrium separation distance between the and the ions in an crystal. Use a value of 41.99 g/mol for the molar mass of and use a value of 2.56 g/cm3 for the density of an crystal.

Q3:

The separation between hydrogen atoms in a molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV. Use a value of J⋅s for the value of the Reduced Planck Constant, and a value of for the value of the unified atomic mass units.

• A eV
• B eV
• C eV
• D eV
• E eV

Q4:

The crystal structure of caesium iodide is body-centered cubic. A ion occupies a cubic volume of , where is the equilibrium separation of ions in the crystal. What is the distance of a ion to its “nearest neighbor” ion if nm?

Q5:

A diatomic molecule with an equilibrium separation of 0.14 nm is in the state.

What is the energy of the molecule?

• A eV
• B eV
• C eV
• D eV
• E eV

How much energy is radiated in a transition from a to a state?

• A eV
• B eV
• C eV
• D eV
• E eV

Q6:

An H2 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

Q7:

A molecule oscillates at a frequency of 88 THz. What is the difference between its adjacent energy levels?

Q8:

The separation between nitrogen atoms in an molecule is 0.11 nm. Determine the characteristic energy of rotation in electron volts. Use a value of 14 u for the atomic mass of .

• A electron volts
• B electron volts
• C electron volts
• D electron volts
• E electron volts

Q9:

The potential energy of a crystal is eV per ion pair. Find the dissociation energy for three moles of the crystal.

• A J
• B J
• C J
• D J
• E J

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⋅m2
• B kg⋅m2
• C kg⋅m2
• D kg⋅m2
• E kg⋅m2

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⋅m2
• B kg⋅m2
• C kg⋅m2
• D kg⋅m2
• E kg⋅m2

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⋅m2
• B kg⋅m2
• C kg⋅m2
• D kg⋅m2
• E kg⋅m2