513.001 Molecular and Solid State Physics

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Physical
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Periodic System
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Average electron energy in 2-D

For a metal at a temperature of T = 0 K, the conduction electrons at the bottom of the band have an energy E = 0 and the conduction electrons with the highest energy have an energy E = EF. For free electrons in two-dimensions, what is the average energy of the conduction electrons?

The density of states for free electrons in 1, 2, and 3 dimensions is given in the table below.