Question

The kinetic energy of a 3-dimensional gas of \(N\) free electrons at 0 K is:

• A. \(\frac{3}{5} N E_F\)
• B. \(\frac{2}{5} N E_F\)
• C. \(\frac{3}{8} N E_F\)
• D. \(\frac{9}{8} N E_F\)

Hint:

For free electron gases, the factor 3/5appears due to the uniform distribution of electrons in momentum space up to EF .

Answer 1

The Correct Option is A

The total kinetic energy of $N$ free electrons in a 3D gas at 0 K is:
\[E_{\text{total}} = \frac{3}{5} N E_F\]
where $E_F$ is the Fermi energy. This result comes from integrating the energy density over the occupied states in the Fermi sphere.