Discussion
The molecular population is :
Answer: C
The population of rotational level J is proportional to (2J + 1)e−E/kT.
Two factors combine. Level J has 2J + 1 degenerate states (MJ = −J ... +J), so it can hold proportionally more molecules; and each state is populated according to the Boltzmann factor e−E/kT, which falls with energy. Their product rises at first and then falls, which is why rotational spectra show a maximum in intensity at an intermediate J.
Option A omits the Boltzmann factor and inverts the degeneracy. Option B divides by the Boltzmann factor, so higher levels would be more populated, and option D both inverts the degeneracy and reverses the sign of the exponent.
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