1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculating chemical potenntial

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the chemical potential, [tex]\mu[/tex] (in units of [tex]\hbar\omega[/tex]) at T = 0 K of 44 [tex]^{6}Li[/tex] atoms with spin 1/2 contained in a 3D harmonic potential well (energy levels, [tex]\epsilon_{i}=(i+3/2)\hbar\omega[/tex] with degeneracies [tex]g_{i}= 1/2(i+1)(i+2)[/tex] )?

    2. Relevant equations


    3. The attempt at a solution

    spin = 1/2 [tex]\Rightarrow[/tex] Fermoins

    t=0 [tex]\Rightarrow[/tex] [tex]\mu=\epsilon_{f}[/tex] (fermi energy)

    a74431b34814575af95738dd8de59715.png = 1/2

    So i need 'i' to then use in [tex]\epsilon_{i}=(i+3/2)\hbar\omega[/tex] to obtain [tex]\mu[/tex].

    I know that [tex]\frac{n_{i}}{g{i}} = 1/2[/tex] and that [tex]g_{i}= 1/2(i+1)(i+2)[/tex] so all i need is the value of [tex]n_{i}[/tex], which is the number of particles in each [tex]g_{i}[/tex].

    Is this all correct? If how do i obatin [tex]n_{i}[/tex]?
  2. jcsd
  3. Dec 7, 2009 #2
    Anyone got any ideas?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook