# Energy distribution of atoms in metal.

1. Mar 28, 2013

### 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?

2. Mar 28, 2013

### Mandelbroth

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.

3. Mar 28, 2013

### DrDu

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.