Question

(d) Using the fact that there is one electron per energy state up to the Fermi energy, Ef, and that the total number of electrons in the volume V of the metal, is given by

? = ∫ ?(?)?? (boundaries ?f top, 0 bottom of integral) show that ?f = (ℏ^2/2?)* (( 3?^2 ?)/ ?)^ 2/3

Estimate the value of the Fermi energy at T = 0 K for aluminium, assuming the density, p = 2.7 g/cm^3,the atomic mass is 26.98 g/mol and the electronic configuration is

1s^2 2s^2 2p^6 3s^2 3p^1

Answer 1