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Don't understand state number

  1. Dec 21, 2008 #1

    KFC

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    In textbook of statistical mechanics, there is an example considering an idealization of a crystal which has N lattice points and the same number of interstitial positions (places between the lattice points where atoms can reside). Let E be the energy necessary to remove an atom from a lattice site to an interstitial position and let n be the number of
    atoms occupying interstitial sites in equilibrium. Now try to find the number of state

    It is quite easy to think about this: choose n atoms from N atoms to fill n interstitial positions, number of possible configuration is given by combination


    [tex]C_{N}^n = \frac{N!}{n!(N-n)!}[/tex]

    I think the number of state should be

    [tex]\Omega = C_{N}^n = \frac{N!}{n!(N-n)!}[/tex]

    but the example just put

    [tex]\Omega = \left(C_{N}^n\right)^2 = \left(\frac{N!}{n!(N-n)!}\right)^2[/tex]

    without saying why. Do you think it is a mistake?
     
  2. jcsd
  3. Dec 21, 2008 #2

    tiny-tim

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    Hi KFC! :smile:

    the atoms have to come from somewhere,

    and they've left gaps behind them …

    so there are NCn ways of choosing where they're from, and NCn ways of choosing where they're going. :wink:
     
  4. Dec 21, 2008 #3

    KFC

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    Got it. Thanks tiny-tim, you help me a lot.
     
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