Question concerning the Sommerfeld Model

Physics Q&A
1

Hi!

I have a question about the graph in which the number of electrons is approximated by the triangles in the Sommerfeld model. If I am correct the electrons in the blue triangle are, due to T > 0, actually in the orange triangle. What I don’t understand is why then N_exc = g(e_F)KbT. Shouldn’t there be a factor 1/2 in front of g(e_F)? Because with N_exc = g(e_F)KbT we are calculating the ‘surface’ of the rectangle formed by the blue and orange triangles, right? Or are there electrons in the blue and orange triangles instead of just in the orange one? Or does a factor of 1/2 not matter in the approximation?

Thank you!

Kind regards,
Charlie

2

In order to derive the dependency on T (by approximation), all the numerical factors are ignored, since they are not needed. Therefore the 1/2 is ignored, since this won’t influence the dependency on T.

1 Like
3

I 100% confirm @stijnvanderlippe’s answer: this is a rough estimate, we aren’t after factors of 1/2 here.

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4

Thank you both, it is clear now!