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 decreases as the quantum number becomes larger.
  • BIt is a constant.
  • CNone of these choices.
  • DIt increases as the quantum number becomes larger.

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 = 3
  • C 𝐽 = 3 to 𝐽 = 4
  • D 𝐽 = 4 to 𝐽 = 5

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

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