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Molecules and Crystals

Problem 6.173

Find the number of rotational levels per unit energy interval, dN/dE,d N / d E, for a diatomic molecule as a function of rotational energy E.E . Calculate that magnitude for an iodine molecule in the state with rotational quantum number J=10.J=10 . The distance between the nuclei of that molecule is equal to 267pm267 \mathrm{pm}.

Reveal Answer
6.173. dN/dE≈VI/2ℏ2E‾d N / d E \approx V \overline{I / 2 \hbar^{2} E}, where II is the moment of inertia of the molecule. In the case of J=10dN/dE=1.0⋅104J=10 d N / d E=1.0 \cdot 10^{4} levels per eV\mathrm{eV}.
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