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Statistic mechanics - particles with energy 0

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    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)) ?



    2. Relevant equations
    No idea how to go about this



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 26, 2009 #2

    Redbelly98

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    Re: stats

    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.
     
  4. Apr 27, 2009 #3
    Re: stats

    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...
     
  5. Apr 27, 2009 #4

    Redbelly98

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    Re: stats

    Yes, that's the one.
     
  6. Apr 29, 2009 #5
    Re: stats

    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.
     
  7. Apr 29, 2009 #6

    Redbelly98

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    Re: stats

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

    P(E=-ε) / P(E=+ε)
     
  8. May 3, 2009 #7
    Re: stats

    Was stuck at this too! I get it now. Thanks!
     
  9. May 4, 2009 #8
    Re: stats

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