The Fermi energy of copper is 7.06 eV. For copper at 1050 K we have to find (a) the energy at which the occupation probability is 0.910. For this energy, we have to evaluate (b) the density of states and (c) the density of occupied states.

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(a)

The Fermi-Dirac probability function is

,

where is the Fermi energy.

The Fermi energy of copper is

.

For copper at 1050 K we have to find the energy at which the occupation probability is 0.910. We solve the equation

(b)

We recall from problem 788. Problem 53.1 (RHK) that the density of states for quantum electron gas is given by the relation

Therefore, the density of states at will be

(c)

The density of occupied states will be