Thermal Physics – Conduction Electrons

The mean kinetic energy of the conduction electrons in metals is ordinarily much higher than kT because

A. electrons have many more degrees of freedom than atoms do
B. the electrons and the lattice are not in thermal equilibrium
C. the electrons form a degenerate Fermi gas
D. electrons in metals are highly relativistic
E. electron interact strongly with phonons

(GR0177 #76)

Solution:

The mean kinetic energy of electrons in metals at room temperature is usually many times the thermal energy kT due to Pauli’s exclusion principle.

According to classical physics, the mean thermal energy of the electrons is ³⁄₂kT.

According to quantum physics, the mean energy of electrons (fermion energy) is  ³⁄₅E_F
where

n = N/a³→ the number of electrons per unit volume

If E_F ≪ kT : electrons are hot (high T) → electrons are non-degenerate → classic (Maxwell-Boltzman) statistic.

In reality, E_F ≫ kT: electrons are cold (room T) → electrons are degenerate → quantum (Fermi-Dirac) statistic.

Answer: C