Someone argues: "Ammonia,

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Invariance, Ch Character tables at work: vibrations, selection rules and splitting

Problem

Someone argues: "Ammonia, NH3\mathrm{NH_3}, has N=4N=4 atoms, so it has 3N−6=63N-6=6 vibrational degrees of freedom. Therefore its infrared and Raman spectra should each show up to six distinct fundamental bands." Find the error in this reasoning and state the correct number of distinct vibrational frequencies for NH3\mathrm{NH_3}.

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