Question

Show that the average energy of an electron in a metal is 3 5 at T = 0 K.

Answer 1

Explanation:

For a free electron gas at T=0K, the average energy per electron is known to be 35EF where EF is the Fermi Energy. When first attempting to derive this, I thought that the average energy per electron could be expressed as (∫EF0dE∗D(E)∗E)/N where N is the total number of electrons. But for some reason it is needed to divide this quantity (without the N) by ∫EF0dE∗D(E). Is this true because ∫EF0dE∗D(E)=N