PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra
Deriving the Spectrum, Ch Polyatomic molecules: normal modes and symmetry
Problem
Methane, CH4 (point group Td), is present in the atmosphere at about 1.9ppm by volume, roughly 200 times less abundant than carbon dioxide's 420ppm. Its four fundamentals have the species and wavenumbers ν1 (A1, 2917cm−1), ν2 (E, 1526cm−1), ν3 (T2, 3019cm−1) and ν4 (T2, 1306cm−1).
((a)) Using the dipole selection rule, state which of the four fundamentals are infrared active, and which are not.
((b)) Contrast this with a heteronuclear diatomic molecule such as HCl: explain why its single vibration is automatically infrared active, in a way that is not automatic for a polyatomic molecule.
((c)) Earth's surface at 288K emits most strongly, per unit wavenumber, near 565cm−1, with about three quarters of the power between 400 and 1400cm−1. State which of methane's infrared-active fundamentals overlaps this range and which does not, and say why ν1 and ν2 contribute nothing to absorbing this radiation however abundant methane becomes.