Please help 4 In the free electron model how does the averag

4. In the free electron model, how does the average electron group velocity compare with the Fermi energy at zero temperature in 2D? (Hint: you will have to use the 2D density of states). (4 marks)

Solution

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.

Confusingly, the term \"Fermi energy\" is often used to refer to a different but closely related concept, the Fermi level (also called electrochemical potential).^[1] There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state, then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature.