# The Boltzmann distribution of uniformly spaced energy levels

by corr0105
Tags: boltzmann, distribution, energy, levels, spaced, uniformly
 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: $$_{}p*$$j=probability that a particle is in state j =exp(-$$_{}E$$j/KT) / $$\sum$$exp(-$$_{}E$$j/KT) I created my own expression for the energy state Ej: $$_{}E$$j=3.2x10^-20(j-1) 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
 Sci Advisor HW Helper PF Gold P: 2,532 Your Boltzmann distribution function has a couple of minus signs missing.
 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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