Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Thermal populations of atomic energy eigenstates

  1. Jul 10, 2009 #1
    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. jcsd
  3. Jul 10, 2009 #2

    diazona

    User Avatar
    Homework Helper

    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
    [tex]P(\psi) = \frac{1}{Z}e^{(N\mu - \epsilon)/kT}[/tex]
    where [itex]\mu[/itex] is the chemical potential of a given state, [itex]\epsilon[/itex] is its energy, [itex]N[/itex] is the number of electrons in the state, [itex]T[/itex] is the temperature, and [itex]k[/itex] 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.
     
  4. Jul 10, 2009 #3
    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.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Thermal populations of atomic energy eigenstates
Loading...