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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