All Problems Molecules and Crystals
Problem 6.173
Find the number of rotational levels per unit energy interval, \(d N / d E,\) for a diatomic molecule as a function of rotational energy \(E .\) Calculate that magnitude for an iodine molecule in the state with rotational quantum number \(J=10 .\) The distance between the nuclei of that molecule is equal to \(267 \mathrm{pm}\).
6.173. \(d N / d E \approx V \overline{I / 2 \hbar^{2} E}\), where \(I\) is the moment of inertia of the molecule. In the case of \(J=10 d N / d E=1.0 \cdot 10^{4}\) levels per \(\mathrm{eV}\).