Understanding Energy Differences in Free Electron Metals

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Homework Statement

a) Explain why in a free electron metal it is not possible for all electrons to have the same energy.

b) Why is the specific heat of simple metals at room temperature much lower than that calculated for a classical gas of electrons?

The Attempt at a Solution

a) Because there are conduction and valence electrons which have different energies. Also draw some graph showing the range o energies electrons can have - but then, how would I explain the graph of g(E) vs E that is a curve?

 

[rude man]

Your g(E) vs. E is presumably the Fermi-Dirac distribution. Its provenance can't be explained in a short posting. It includes the Pauli exclusion principle and applies to all fermions, not just electrons.