Rotational spectra - thermal population of rotational levels

  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.
     
    Last edited: Apr 19, 2007
  2. jcsd
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