513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
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Calculate the Fermi energy of a metal

What is the relationship between the electron density and the Fermi energy in the free electron model? Explain how this relationship would be derived.

Hint: The volume in k-space corresponding to one allowed k-state is ((2π)/L)³, where L is the length of the crystal. The total volume of the crystal is L³. There are twice as many electrons states as k-states due to spin.