# Boltzmann Factor Type Question

1. Feb 25, 2013

### ferret123

1. The problem statement, all variables and given/known data

A system in thermal equilibrium at temperature T consists of N particles that have two
energy states separated by an energy Δε.

If the number of particles in the two states is N1 and N2, show that:

$N{1}$ = N($\frac{1}{1+exp(-Δε/k{B}T}$)) and $N{2}$ = N($\frac{exp(-Δε/k{B}T}{1+exp(-Δε/k{B}T}$))

2. Relevant equations
$\frac{N{1}}{N{2}}$ = $\frac{exp(-E{1}/k{B}T}{exp(-E{2}/k{B}T}$

Δε=E1 - E2

3. The attempt at a solution

Really struggling to see where to get started with this the lectures and the lecture notes we have are not helping.

2. Feb 25, 2013

### TSny

From the way the problem is worded, I think Δε should be Δε = E2 - E1

See if you can show $\frac{N{2}}{N{1}}= {exp(-Δε/k_{B}T)}$

Also, what must the sum N1+N2 equal?

Last edited: Feb 25, 2013
3. Feb 25, 2013

### ferret123

Well N1 + N2 must equal N?

So now that I have it in terms of Δε I can rearrange for expressions for N1 and N2 then add them for N?

4. Feb 25, 2013

### TSny

You have two equations for N1 and N2. So you should be able to solve for N1 and N2 separately.