Has nuclear spin (a boson) and has nuclear spin (a fermion); both are in a ground…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Molecular structure and spectra

Deriving the Spectrum, Ch Diatomic rotation-vibration spectra and nuclear spin statistics

Problem

6Li2^6\mathrm{Li}_2 has nuclear spin I=1I=1 (a boson) and 15N2^{15}\mathrm{N}_2 has nuclear spin I=12I=\tfrac12 (a fermion); both are in a 1Σg+^1\Sigma_g^+ ground electronic state. ((a)) Predict the ratio of the statistical weights of even- to odd-JJ rotational levels for each molecule, and state whether any levels are missing entirely. ((b)) State whether either molecule shows a pure rotational absorption spectrum or an infrared vibrational fundamental, and why.

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