Free Electron Model - Fermi Level

Fermi Level

According to the Pauli principle, the electrons in the ground state occupy all the lowest-energy states, up to some Fermi energy . Since the energy is given by

,

this corresponds to occupying all the states with wave vectors, where is so-called Fermi wave vector, given by

,

where is the total number of electrons in the system, and V is the total volume. The Fermi energy is then

In a nearly-free-electron model of a -valent metal, one can replace with, where is the total number of metal ions.