Use the partition function for a harmonic oscillator, q = 1 / (1 - e^-hv/kBT), to determine the ratio of populations in the lowest and first excited energy levels, P0/P1, for the indicated systems at two temperatures, 50 K and 298 K:
(a) The 1700 cm-1 stretching vibrational mode for the carbonyl (C=O) group in the peptide bond of a polypeptide.
(b) the 150 cm-1 torsional vibrational mode for the C=C bond in trans-2-butadiene.
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