Problem 6.174

Find the ratio of energies required to excite a diatomic molecule to the first vibrational and to the first rotational level. Calculate that ratio for the following molecules:

Molecule $\omega, 10^{14} \mathrm{~s}^{-1} \quad d, \mathrm{pm}$

(a) $\mathrm{H}_ {2}$ $8.3 \quad 74$ (b) HI $4.35 \quad 160$ (c) $\mathrm{I}_ {2}$ $\begin{array}{ll}040 & 267\end{array}$

Here $\omega$ is the natural vibration frequency of a molecule, $d$ is the distance between nuclei.