Question

1. Sodium has mass number 22.9 and density 970 kg/m^3.

Find a) free electron concentration.

b) fermi wave number

C) fermi energy and velocity.

Answer 1

a)

$n=\frac{\rho N_A}M=2.5\cdot 10^{28}~m^{-3},$

b)

$k=(3\pi^2 n)^{\frac 13}=9\cdot 10^9~m^{-1},$

c)

$E=\frac{h^2k^2}{8\pi^2m_e}=3.1~eV,$

$v=\frac{hk}{2\pi m_e}=10^6~\frac ms.$