Cu is a face-centered-cubic ( * fcc * ) metal with one valence electron per atom.

(a) Look up the density of copper, its atomic mass, Avogadro's number, and from these calculate the number of valence electrons/unit volume ( * N * / * V * ).

(b) From these numbers, calculate a numerical value for the Fermi energy ( * E _{ F } * ) at absolute zero (

(c) Evaluate the density of states in energy * g * ( * E * ) at the Fermi energy in “states per atom per electron volt". Try to find g(E) as a function of \(E_F \) and \(N\), and since we are looking at the density of states per atom you can plug in \(N=1\).

(d) Given that * k _{ B } T * = 1/40 eV at room temperature, use your numerical result from part (c) to estimate the number of states per atom within

Try to estimate the number of states in the region \(E\in[\mu-K_BT,\mu + K_BT]\) by the relation \(\Delta N=g(\varepsilon)\Delta E \)