# Compute the Fermi energy and momentum at absolute zero

Fermi energy and wavevector for a gas at absolute zero.

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#### Solution Preview

It is simplest to solve these kind of problems by using the fact that the number of momentum states of a free particle in a volume V is given by:

N = Vp V/h^3 (1)

Here Vp is the volume in momentum space that the particle can be in, and h is the ordinary Planck's constant. Electrons are spin 1/2 particles, so an electron in some given momentum state can be in two spin states. So, the total number of quantum states available to an electron given that it is in some volume Vp of momentum space and a volume V in ordinary space is given by:

N = 2 Vp V/h^3

This is valid in 3 dimensions. In d dimensions the formula becomes:

N = 2 Vp V/h^d (2)

We can find the Fermi momentum for a 3 dimensional free electron gas as follows. The Fermi momentum is, by definition, the largest momentum of the state that you get when ...

#### Solution Summary

We show how to compute the Fermi energy, momentum and temperature. We give the figures for the case of Copper.