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Radius of Fermi Sphere 
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#1
May110, 07:04 PM

P: 12

1. The problem statement, all variables and given/known data
Problem 9.2(B) from Kittel Solid State Physics. A twodimensional metal has one atom of valence one in a simple rectangular primitive cell of a1 = 2Å and a2 = 4Å. Calculate the radius of the free electron Fermi sphere and draw this sphere to scale on the drawing of the Brillouin zones. A 2D solution that seems to be correct is posted here . Can anyone tell me what is wrong with my approach? Also, some equations weren't working for the latex. Sorry. 3. The attempt at a solution First I find the electron concentration in terms of [itex]k_{F}[\latex] [itex]V=(4/3) \pi k^{3}[/itex] [itex]N=2*(4/3)*\frac{\pi k^{3}}{V_{k}}[/itex] where V_{k}=\frac{2 \pi}{a}*\frac{2 \pi}{a}*\frac{2 \pi}{b}=\frac{4 \pi^{3}}{a^{3}} (latex code didn't work for this) which is the kspace volume. The factor of 2 is the electron spin degeneracy. The electron concentration, N, is then: [itex]N=\frac{8}{3}\frac{\pi k^{3}a^{3}}{4\pi^{3}}=\frac{2k^{3}a^{3}}{3\pi^{2}}[/itex] which gives [itex]k=(\frac{3\pi^{2}N}{2a^{3}})^{1/3}[/itex] using N=1 and plugging in the values for a and b I get. k=(3\pi^{2})/16 (the latex code is screwing up for some reason) This gives me 1.23 A^1. Where did I go wrong? 


#2
May110, 11:21 PM

P: 675

Why is your momentum space 3d when the problem is 2d?



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