Question

A particular metal has 1022 electrons per cubic centimeter. calculate the fermi energy

Answer 1

We have to find Fermi energy of a particular metal, if electron density of the metal is 10²² /cm³.

solution : Fermi energy is given by,

$E_F=\frac{(hc)^2}{2mc^2}\left(\frac{3N}{8\pi V}\right)^{2/3}$

here (hc) = 1240 eV nm

mc² for electrons in eV = 0.511 × 10⁶ eV

N/V = 10²² /cm³ = 10²²/(10^7 nm)³ = 10 / nm³

now, E = (1240)²/(2 × 0.511 × 10⁶) × [(3 × 10)/(8π)]⅔

= 1.6929 eV ≈ 1.7 eV

Therefore the Fermi energy of the metal is 1.7 eV