Worksheet: Rovibrational Energy Levels

In this worksheet, we will practice calculating diatomic energy level spacings from the vibrational frequency and rotational and centrifugal constants.

Q1:

Which of the following statements accurately describes the energy gap between two adjacent quantum states in a rigid rotor system?

  • AIt increases as the quantum number becomes larger.
  • BIt is constant.
  • CIt decreases as the quantum number becomes larger.
  • DNone of these choices.

Q2:

In a typical rotational–vibrational absorption spectrum with a 𝑣=0 to 𝑣=1 transition, which of the following lines occurs at the highest frequency?

  • A 𝐽 = 0 to 𝐽=1
  • B 𝐽 = 4 to 𝐽=5
  • C 𝐽 = 4 to 𝐽=3
  • D 𝐽 = 3 to 𝐽=4

Q3:

In a typical rotational–vibrational absorption spectrum with a 𝑣=0 to 𝑣=1 transition, which of the following lines occurs at the lowest frequency?

  • A 𝐽 = 1 to 𝐽=0
  • B 𝐽 = 4 to 𝐽=3
  • C 𝐽 = 3 to 𝐽=4
  • D 𝐽 = 0 to 𝐽=1

Q4:

The vibrational frequency of the oxygen molecule is 4.741×10 s−1. In the vibrational partition function, the energy of the lowest vibrational energy level is set to zero and all other vibrational energies are calculated relative to this value. Using the harmonic oscillator approximation, calculate to 4 significant figures the vibrational partition function for the oxygen molecule at 1,000 K.

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