# Thermal populations of atomic energy eigenstates

1. Jul 10, 2009

### Kazza_765

Basically I have an (infinite) population of isolated atoms with a bunch of discrete energy levels available to them. I want to work out what the expected population of each of the states is at a given temperature.

They're complex atoms (transition metals) and spin-orbit coupling combined with various valance configurations gives me a big spectrum of possible eigenstates, with a number of different degeneracies. I'm sure I should have covered this at some stage in my education, but I always hated statistical physics and skipped most of the lectures.

I'm hoping someone could point me towards the right formula or the right book, or even a paper that has covered this at a basic level and has useful references. The only thing I remember is looking at the fermi level in semi-conductors, but I don't think that applies when we have discrete states.

Thanks
John

2. Jul 10, 2009

### diazona

The book I always liked for statistical mechanics, at least as an introduction, was "An Introduction to Thermal Physics" by Daniel Schroeder. So you might have a look at that. Basically you're going to need something like
$$P(\psi) = \frac{1}{Z}e^{(N\mu - \epsilon)/kT}$$
where $\mu$ is the chemical potential of a given state, $\epsilon$ is its energy, $N$ is the number of electrons in the state, $T$ is the temperature, and $k$ is Boltzmann's constant. I'm not sure if that's the exact notation used in the book but it should be recognizable at least.

3. Jul 10, 2009

### Kazza_765

Terrific, thankyou very much. Off to the library now.

(I reckon it's always better to have someone recommend a good book than just typing "statistical physics" in the catalogue.)