Problems

$1-$ The density of states function for electrons in a metal is given by:

$g(E)dE=13\mathrm{.}6{10}^{27}{E}^{\frac{1}{2}}dE$

Where $E$ is measured in $eV$ and the mass of electron is $9\mathrm{.}11{10}^{-31}kg.$ Calculate

a$)$ the Fermi level energy for copper which has $8\mathrm{.}5{10}^{28}$ electrons per cubic metre.

b$)$ the velocity of electrons at the Fermi level in copper.

$2-$ Copper, being a metal, has a sea of free electrons. Calculate the Fermi energy of copper given that;

The mass of the electron is $9\mathrm{.}11{10}^{-31}kg,$ number of charges per unit volume is $8\mathrm{.}5{10}^{28}$ electrons per cubic metre and $h=1\mathrm{.}04{10}^{-34}J.s.$