# Rotational spectra - thermal population of rotational levels

by isomer
Tags: levels, population, rotational, spectra, thermal
 P: 1 1. The problem statement, all variables and given/known data If the thermal population of the rotational levels is given by: Nj/No = (2J+1)*exp(-hcBJ(J+1)/kT) Calculate which state has the highest thermal population at a given temperature T. Calculation needs to be shown, not just a result. 2. Relevant equations Nj/No = (2J+1)*exp(-hcBJ(J+1)/kT) where: Nj = population in excited j state No = population in ground state J = rotational quantum # B = rotational constant k = Boltzmann constant T = temperature 3. The attempt at a solution I honestly don't know where to even begin..... The given equation appears to be in the form of a Boltzmann distribution. I'd assume a reasonable answer would be a function of J and T; where the function is greater than 1, obviously the Nj state would have the highest thermal population and vice versa. Other than that, i'm pretty much at a loss. Took a stab in the dark, differentiating the right side of the equation with respect to J then setting equal to zero to maximize the function and get it down to a single variable, temperature, but I seem to be getting nowhere fast. Any help would be greatly appreciated, thanks.

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