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CAF123
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Homework Statement
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.
Homework Equations
Sommerfeld model, ##c_v = \pi^2/2 (k_B T/\epsilon_f) k_B## per electron in sample.
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