Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 1 / A3 / b / ii / Solution

Count the successive Q branch lines from the low-frequency edge, taking $J=1$ as the first allowed bend transition; the first lines are crowded and partly unresolved. The maximum near $712.55{\mathrm{cm}}^{-1}$ is approximately $J=12$. Treating $J$ as continuous in the intensity envelope from part (i),HenceUsing $hc/k_{\mathrm{B}}=1.43878\mathrm{K}\mathrm{cm}$, $B^{\prime \prime }=1.47786{\mathrm{cm}}^{-1}$ and $J_{\max }\simeq 12$ givesA useful check avoids locating the exact maximum. The plotted $J\simeq 20$ line has roughly $0.70$ of the $J\simeq 12$ peak height. Thusgives about $659\mathrm{K}$. An appropriate graphical estimate is $T\simeq 6.6\times 10^2\mathrm{K}$, with precision limited by line counting, line overlap and reading the plotted intensities. There is no basis for reporting a temperature to the nearest kelvin from this figure.