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Calculating The Fermi Energy - Condensed Matter Physics

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  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data
    Calculate the Fermi energy, EF at 0K for potassium (atomic weight = 39, density = 860 kgm3).

    2. Relevant equations
    KF3 = 3π2n
    Fermi Momentum ρ = h(bar)KF

    3. The attempt at a solution:
    For the first part:

    Using: E = ρ2/ 2m
    Can substitute Fermi momentum into that to get:

    EF = h(bar)2 KF2 / 2m

    KF2 = √(3π2n) = π√(3n)

    Putting all the together I got:

    EF = h(bar)2 π √(3n) / 2m

    which is the same as: EF = h2 √(3n) / 4m

    I'm not too sure what to do after this point as i'm not sure how the atomic weight or density can give me a value for n and m. I do have written in my notes that n = N/v but again I wasn't sure how this would help me. I feel like I must be going down the wrong path to come out with an equation that needs completely different things to what the question is providing me with. But honestly I have just started this condensed matter course and haven't really got my feet yet.


    Thanks in advance to anyone that replies.

     
  2. jcsd
  3. Feb 3, 2015 #2

    TSny

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    Homework Helper
    Gold Member

    You haven't solved for KF2 correctly. What do you get if you first solve for KF?
    n is the number of atoms per unit volume, whereas mass density ρ is the mass per unit volume. Try to think of a way to relate n to ρ using the atomic mass, matom.
     
  4. Feb 5, 2015 #3
    Ooops yes not sure what i was thinking there. Thank you for your help i think i've cracked it now.
     
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