# Fermi energy

## Homework Statement

Calculate the Fermi energy for magnesium, assuming two free electrons per atom.

## Homework Equations

${E_F} = \frac{{{\hbar ^2}}}{{2m}}{(3{\pi ^2}\rho )^{2/3}}$, where $\rho = q\frac{N}{V}$ and q is the number of free electrons.

## The Attempt at a Solution

q = 2, so $\rho = 2\frac{N}{V} = 2\left( {\frac{{{\text{atoms}}}}{{{\text{mol}}}}} \right)\left( {\frac{{{\text{mol}}}}{{\text{g}}}} \right)\left( {\frac{{\text{g}}}{{{\text{volume}}}}} \right) = 2\frac{{{N_A}}}{M}\frac{m}{V}$.

i.e. $2\left( {\frac{{{\text{the Avogadro constant in mo}}{{\text{l}}^{ - 1}}}}{{{\text{molar mass in g/mol}}}}} \right)\left( {{\text{density in g/c}}{{\text{m}}^3}} \right)$.

etc.

Is this the right approach? Is the formula for ${E_F}$ correct?