Calculating Fermi Energy for Magnesium

In summary, to calculate the Fermi energy for magnesium with two free electrons per atom, you can use the formula {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, with units of electrons per atom. Your approach and calculations are correct.
  • #1
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Homework Statement



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

Homework 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.

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?
 
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  • #2




Your approach and formula for calculating the Fermi energy for magnesium are both correct. The formula you provided is the correct expression for the Fermi energy, also known as the Fermi level, in a system with two free electrons per atom. The only thing to note is that the units for q should be in units of electrons per atom, not just the number 2. Other than that, your calculations are correct. Keep up the good work!
 

1. What is the formula for calculating Fermi Energy for Magnesium?

The formula for calculating Fermi Energy for Magnesium is EF = (h2/8m)(3π2n)2/3, where h is Planck's constant, m is the mass of an electron, and n is the electron density.

2. How do you determine the electron density for Magnesium?

The electron density for Magnesium can be determined by dividing the total number of valence electrons by the volume of the crystal lattice. This can be found by using the Avogadro's number and the molar mass of Magnesium.

3. What is the significance of calculating Fermi Energy for Magnesium?

Calculating Fermi Energy for Magnesium helps determine the energy level at which the electrons in the material are completely filled. This information is important in understanding the material's conductivity, as well as its electronic and magnetic properties.

4. Are there any assumptions made when calculating Fermi Energy for Magnesium?

Yes, there are some assumptions made when calculating Fermi Energy for Magnesium. These include assuming the material is in thermal equilibrium, and that the electronic energy levels are described by the free electron model.

5. Can Fermi Energy for Magnesium be experimentally measured?

Yes, Fermi Energy for Magnesium can be experimentally measured using techniques such as photoemission spectroscopy or tunneling spectroscopy. These techniques involve measuring the energy of the electrons in the material and can provide accurate results for Fermi Energy.

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