# Energy distribution of atoms in metal.

by BarryRE
Tags: atoms, distribution, energy, metal
 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?
P: 597
 Quote by BarryRE 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.
 Sci Advisor P: 3,375 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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