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Electronic partition function for molecule with degeneracies 
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#1
Mar1212, 02:46 PM

P: 3

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[(EiEi1)/(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 @3500cm1, g2=3@4700cm1 I came up with the equation qel= 3+ 1*exp[(E1E0)/(kbT)] + 3*exp[(E2E1)/(kbT)] T= 2000K, kb= boltzmann constant ~1.38e23 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
Mar1212, 10:44 PM

HW Helper
P: 2,327

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.) 


#3
Mar1312, 12:12 PM

P: 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



#4
Mar1312, 08:16 PM

Mentor
P: 12,070

Electronic partition function for molecule with degeneracies



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