Question

Calculate the Fermi energy of sodium at 0 K if it has one free electron per
atom and density 970 kg/m3 and atomic weight 23.

Answer 1

$$n_c=\frac{N\rho}{M}=\frac{6.02\cdot10^{26}(970)}{23}=2.5\cdot10^{28}\ m^{-3}$$

$$E_F(0)=\frac{h^2}{2m}\left(\frac{3n_c}{8\pi}\right)^{\frac{2}{3}}=\frac{(6.625\cdot10^{-34})^2}{2(9.11\cdot10^{-31})}\left(\frac{3(2.5\cdot10^{28})}{8\pi}\right)^{\frac{2}{3}}$$

$$E_F(0)=5.11\cdot10^{-19}J=3.1\ eV$$