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Energy distribution of atoms in metal.

by BarryRE
Tags: atoms, distribution, energy, metal
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BarryRE
#1
Mar28-13, 07:04 AM
P: 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?
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Mandelbroth
#2
Mar28-13, 03:48 PM
Mandelbroth's Avatar
P: 615
Quote Quote by BarryRE View Post
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?
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.
DrDu
#3
Mar28-13, 03:57 PM
Sci Advisor
P: 3,593
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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