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Homework Statement
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.
Homework 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
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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