1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Rotational spectra - thermal population of rotational levels

  1. Apr 19, 2007 #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)


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted