### Free Electrons 2

exercise 3_4931

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 ( T = 0) in eV. in order to do that you'll have to find $$E_F$$ as a function of $$\frac{N}{V}$$

(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 k B T of the chemical potential, m , at room temperature ( T = 298 K).

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