Statistic mechanics - particles with energy 0

[captainjack2000]

Homework Statement

System of weakly interacting particles in equilibrium temperature T, each particle can exist in three energy states -epsilon, +epsilon and 0. There are three times as many particles in the -epsilon state as in the +epsilon state. Show that fraction of particles with energy 0 is sqrt(3)/(4+sqrt(3)) ?

Homework Equations

No idea how to go about this

The Attempt at a Solution

 

[Redbelly98]

There's an equation that gives the relative probability, or number, of particles occupying different energy states. Should be in your textbook or class notes ... it contains the number e, as well as T and k.

 

[latentcorpse]

is it along the lines of P(E_i)=e^{-E_i/kT}/(sum_j e^{-E_j/kT})

thats probably wrong but could you confirm please...

 

[Redbelly98]

Yes, that's the one.

 

[aurora14421]

I'm stuck on the same question. I have the expression for the probabilities but I can't get the final expression they have. Any chance of another hint? I've been staring at this for a while and getting nowhere.

 

[Redbelly98]

P(E_i)=e^{-E_i/kT}/(sum_j e^{-E_j/kT})

Use this ↑ equation to write an expression for the ratio:

P(E=-ε) / P(E=+ε)
​

 

[Welshy]

Use this ↑ equation to write an expression for the ratio:

P(E=-ε) / P(E=+ε)
​

Was stuck at this too! I get it now. Thanks!

 

[aurora14421]

Yeah, thanks for the help. I got it too.