PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra
Invariance, Ch Character tables at work: vibrations, selection rules and splitting
Problem
Nitrous oxide, N2O, is a linear triatomic gas with two nitrogen atoms and one oxygen atom. Its structure was once uncertain between two candidates: (i) a symmetric structure N-O-N, with the oxygen atom at the centre, and (ii) an unsymmetrical structure N-N-O, with the two nitrogens adjacent. The measured infrared and Raman spectra of gaseous N2O show three fundamental bands, at 2224cm−1, 1285cm−1 and 589cm−1, and each of the three is recorded in both the infrared absorption spectrum and the Raman spectrum.
((a)) For candidate (i), name its point group, then treat it as CO2 is treated in its finite subgroup D4h (an X-Y-X linear molecule with Γvib=A1g+A2u+Eu), and state which of its three vibrations would be infrared active, which Raman active, and whether any band could appear in both spectra.
((b)) For candidate (ii), name its point group and explain, from the vanishing integral theorem, whether the same exclusivity is forced.
((c)) Decide, from the measured data, which of the two candidate structures nitrous oxide has, and justify the decision.