The density of the electron states in a metal can be written as g(E) = AE^(1/2), where is a constant and is measured from the bottom of the conduction band.
Derive the total number of states in this material and calculate the fraction of conduction electrons ƒ within KT of the Fermi energy for molybdenum at 300 K. Hints: Use the approximation (1- KT/Eꜰ)^(3/2) ≈ 1-(3/2)KT Eꜰ^(1/2).
Calculate the Fermi energy for this metal at 0 K using the expression for the density of electron states. Assume the electronic structure contains 1 electron per atom.