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Energy distribution of atoms in metal.

  1. Mar 28, 2013 #1
    An ideal gas obeys Maxwell Boltzman statistics. Gas atoms
    have an average kinetic energy of 3kT/2 but the individual atoms
    have energies that vary from this average (Chi square distributed).

    A solid (metal) has an average kinetic energy of about 3kT.
    Does anybody know what statistical distribution the energy of
    individual atoms of the metal obey?
  2. jcsd
  3. Mar 28, 2013 #2
    I would conjecture that they would also obey a distribution similar to, if not equivalent to, that of a ##\chi^2## distribution, though the formula would probably be a lot more involved.

    If you want to really know more about this kind of thing, statistical mechanics is the topic you want to look into.
  4. Mar 28, 2013 #3


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    Science Advisor

    After some scaling of the variables, the energy is a sum of six squares:
    ##E=x^2+y^2+z^2+p_x^2+p_y^2+p_z^2##, hence E has also a chisquare distribution but not with 3 but 6 degrees of freedom.
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