Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 1 / A3 / b / iii / Solution

The relevant allowed absorption is $1\to 2$. Under the stipulated population-only intensity model, the vibrational levels are nondegenerate andSet this ratio to $0.10$ and solve:The energy in the exponential is the measured $0\to 1$ gap, not the harmonic constant $444.3\mathrm{c}{\mathrm{m}}^{-1}$. At this temperature, $N_2/N_0\simeq 0.0102$, so considering the first thermally excited manifold is sensible. Actual band intensity ratios also involve transition moments and rotational structure; the calculation follows the question's simplifying assumption.