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The Boltzmann distribution of uniformly spaced energy levels 
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#1
Feb2508, 04:27 PM

P: 7

The question states:
A system has energy levels uniformly spaced at 3.2x10^10 J apart. Thepopulations of the energy levels are given by the Boltzmann distribution. What fraction of particles is in the ground state at T=300K. I know that the Boltzmann distribution is: [tex]_{}p*[/tex]j=probability that a particle is in state j =exp([tex]_{}E[/tex]j/KT) / [tex]\sum[/tex]exp([tex]_{}E[/tex]j/KT) I created my own expression for the energy state Ej: [tex]_{}E[/tex]j=3.2x10^20(j1) My thought process behind this was that to get the energy state of each level you have to multiply by the space between each level times 1 minus the level. In other words, E1=0*3.2x10^20, E2=1(3.2x10^10)...etc. I set this pj* equal to: # particles in ground state (g) / # states (t) Assuming that the particles in the ground state would have energy E=0 I plugged all of the given values into the equation: T=300, Ej=0, K=boltzmann's constant. Because the problem did not give the number of states my answer is in terms of t. I got an answer of: 0.25875/(1+t) Obviously this is wrong because you cannot have a negative number of particles. ANY IDEA WHAT I'VE DONE WRONG??!?!? thanks in advance for any help 


#2
Feb2508, 06:10 PM

Sci Advisor
HW Helper
PF Gold
P: 2,532

Your Boltzmann distribution function has a couple of minus signs missing.



#3
Feb2508, 06:24 PM

P: 7

I'm sorry, you are correct. The post has been edited. It was a typo, but the answer I got still stands.



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