The allowed energies associated with the vibration of a diatomic molecule are given by He...

The allowed energies associated with the vibration of a diatomic molecule are given by

Here, k is the vibrational quantum number and can take the values k = 0, 1, 2 … and f is the resonant frequency of the vibration. In a simple model of diatomic hydrogen H2, the resonant vibration frequency can be taken as f = 1.3 × 1014 Hz.

a. Find the difference in energy between the first excited vibrational energy state and the ground vibrational state of diatomic hydrogen. That is, find . Express the answer in both J and eV.

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b. Find the relative likelihood Pk =1/Pk= 0 that a hydrogen molecule will be in its first excited vibrational state in thermal equilibrium at room temperature, T = 293 K.