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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

    a74431b34814575af95738dd8de59715.png

    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)

    therefore:
    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?
     
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