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Applying the Sommerfeld model

  1. Oct 20, 2014 #1

    CAF123

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    1. The problem statement, all variables and given/known data
    a) From the graph attached (see also Philips book) deduce the Fermi energy for copper using the Sommerfeld model
    b) Estimate ##v_s## in copper, where ##v_s## is the speed of the low temperature phonon vibration.

    2. Relevant equations
    Sommerfeld model, ##c_v = \pi^2/2 (k_B T/\epsilon_f) k_B## per electron in sample.

    3. The attempt at a solution
    So I rewrite the equation above like $$c_v/T = \pi^2/2 (k_B /\epsilon_f)k_B.$$ From the sketch ##C/T = A + BT^2## so at ##T=0, C/T = A## in the given units. Sub this in gives $$\epsilon_f = \frac{\pi^2}{2} \left(\frac{(k_B)^2 (m^2 kg s^{-2}K^{-1})^2}{A \, mJ \, mol^{-1} deg^{-2})}\right) = \frac{\pi^2}{2} \left(\frac{(k_B)^2 J \text{mol}}{A}\right) $$ by cancelling out the units. Then there are avagadro number of atoms in a mole and copper has one conduction electron per atom, so the Fermi energy I get is ##\epsilon_f \times 6.02 \times 10^23 \approx 3.75 eV##. The value I found from another source is about 7eV so the numbers are comparable but I was wondering if my method was right?

    Thanks
     

    Attached Files:

  2. jcsd
  3. Oct 25, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Oct 26, 2014 #3

    CAF123

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    Gold Member

    Hi Greg, yes I have resolved the problem thanks for the bump anyway.
     
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