All Problems Molecules and Crystals
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.
6.174. \(E_{\text {vib }} / E_{r o t}=\omega \mu d^{2} / \hbar,\) where \(\mu\) is the reduced mass of the molecule; (a) \(36 ;\) (b) \(1.7 \cdot 10^{2}\) (c) \(2.9 \cdot 10^{3}\)