The density of states at the Fenni level (7 eV) was calculated for 1 cm3 of a certain metal to be about 1021 energy states per electron volt. Someone is asked to calculate the number of electrons for this metal using the Fenni energy as the maximum kinetic energy which the electrons have. He argues that because of the Pauli principle, each energy state is occupied by two electrons. Consequently, there are 2 x 1021 electrons in that band.
(a) What is wrong with that argument?
(b) Why is the answer, after all, not too far from the correct numerical value?