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Electronic partition function for molecule with degeneracies

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    A atom had a threefold degenerate ground level, a non degenerate electronically excited level at 3500 cm^-1(setting the energy orgin as the ground electronic state energy of the atom ) and a threefold degenerate level at 4700 cm^-1 . Calculate the electronic partition function of this atom at 2000K


    2. Relevant equations

    qel= sumnation{i=0inf}[gel*exp[-(Ei-Ei-1)/(kbT)]]

    3. The attempt at a solution

    I see three levels in the problem
    I believe, given the problem statement, that g0=3, g1=1 @3500cm-1, g2=3@4700cm-1

    I came up with the equation
    qel= 3+ 1*exp[-(E1-E0)/(kbT)] + 3*exp[-(E2-E1)/(kbT)]

    T= 2000K, kb= boltzmann constant ~1.38e-23

    I am having trouble finding the energy values for each excited state. I am not sure if E=hv applies to this problem.

    Also I am not too confident in the equation I found.

    If anyone understands degeneracy, electronic partition functions or excited electronic stateI would greatly appreciate any help
     
  2. jcsd
  3. Mar 12, 2012 #2

    turin

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    Homework Helper

    I would assume that you just use
    E = h f
    = h c / lambda
    = hbar c k
    , no? (I'm assuming that the inverse lengths that the problem specifies are wavenumbers of photons that would be emitted from the corresponding energy differences.)
     
  4. Mar 13, 2012 #3
    yes I guess I can just multiply those numbers by c to get the excited state energies. Doing this it seems that all the exponentials go to zero because kbT is so small and c is so large. I guess the electronic partition function ends up being equal to 3
     
  5. Mar 13, 2012 #4

    Redbelly98

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    There is more to the calculation than just kBT and c. Try calculating the value of [itex]\frac{\Delta E}{k_B T}[/itex] for the two excited states.

    That's pretty much correct, except that it is E2-E0 in the final term.

    Yes, it does.
     
    Last edited: Mar 13, 2012
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