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Partition function

  1. May 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Calculate fermi energy, fermi temp and fermi wave vector.
    a)Protons with n= 1.0E43 [tex] m^{-3} [/tex]
    b) [tex] ^{3}He [/tex] in liquid He (atomic volume= 46E^-3 [tex]m^3[/tex]

    2. Relevant equations
    [tex]E_f=\frac{h^2}{8 m} (\frac{3 n}{\pi V})^\frac{2}{3} [/tex]
    [tex]T_f= \frac{E_f}{k_B}[/tex]

    3. The attempt at a solution
    I get the energy and temp.
    Is the wave vector equation:
    [tex] k=\sqrt{\frac{8 \pi^2 m E_F}{h^2}}[/tex]?
    for the last one [tex] \frac{n}{v}=\frac{3}{ 46E^{-3}}[/tex]?
     
  2. jcsd
  3. May 9, 2009 #2
    You remember [tex]E=\frac{\hbar^2 k^2}{2m}[/tex]. So just replace the energy and wavevector with the Fermi variables, so you are left with:

    [tex]E_F=\frac{\hbar^2 k_F^2}{2m}[/tex]

    For part (b) check the units on the atomic volume. Is it per mole?
     
  4. May 9, 2009 #3
    Not sure. It says [tex]^{3}He [/tex] atoms in liquid [tex]^{3}He [/tex]. So it should be n=3(3fermions) and V=46E-30 m^3. I think that sounds right.
     
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