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Homework Help: Fermi energy

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

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

    3. The attempt at a solution

    q = 2, so [itex]\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}[/itex].

    i.e. [itex]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)[/itex].

    etc.

    Is this the right approach? Is the formula for [itex]{E_F}[/itex] correct?
     
  2. jcsd
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