The transition between the ground and first excited vibrational levels of the ICl molecule is observed at a wavenumber of 381 cm^-¹. Given that the vibrational energy levels of a diatomic molecule such as ICl are singly degenerate, determine the relative populations of the ground and first excited vibrational levels at temperature of 400 K.

Question

Quizplus · Accepted Answer

The relative population of vibrational levels is given by the Boltzmann distribution: $ n_{upper}/n_{lower} = e^{-\Delta E/kT} $. Here, $\Delta E = hc \times 381 \, \text{cm}^{-1}$, $k$ is the Boltzmann constant, and $T = 400 \, \text{K}$. Calculating this gives approximately 0.014.

The Transition Between the Ground and First Excited Vibrational Levels