Condensed Matter Physics - Fermi velocity, etc.

[Graham87]

Homework Statement

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Relevant Equations

See pic

I have made solutions a-d, but my fermi velocity seems too big.

 

[Gordianus]

Have you used Ef= 5 J?
Remember, it's Ef= 5 eV.

 

[Graham87]

Have you used Ef= 5 J?
Remember, it's Ef= 5 eV.

Thanks! I realized that later. When I converted eV to joule I got the right Fermi velocity.

However, how may I got mean electron speed?
I know that most of the electrons are not on the Fermi surface, and I need to find the mean speed of all electrons.

 

[Gordianus]

Do you know something about the density of states function g(E)?

 

[Graham87]

Do you know something about the density of states function g(E)?

We know that density of states in 2D is (L/2pi)^2 ?
So DOS is the no of electrons per unit area? So I just have to multiply DOS with unit area to find the total electrons?
But I will need the velocity of the total electrons?

 

[Graham87]

I think I solved most of my problem now.

However I’m not 100% sure about mean speed in a). I used the formula and plugged in Fermi energy there, but might there be another E that should be there instead?

Thanks