Question

Compute the Fermi energy and the average energy per particle for electrons in copper (you may look up the electron density for copper)

Answer 1

here we need to have the values are

h = 6.6 x 10^-34 J.sec

= h / 2

= 1.055 x 10^-34 J.sec

electron mass m_e = 9.31 x 10^-31 kg

1 eV = 1.6 x 10^-19 J

= 8.49 x 10²⁸ /m³

using the equation for fermi energy

E_F = ² x ( 3 ² )^2/3 / 2 m_e

= (1.055 x 10^-34)² x ( 3 x 8.49 x 10²⁸ x 3.14² )^2/3 / 2 x 9.1 x 10^-31

= 11.2 x 10^-19 J

converting Joule to eV

= 11.29 x 10^-19 / 1.6 x 10^-19

= 11.29 / 1.6

E_F = 7.056 eV