Number of conduction electrons in a Fermi sphere of known radius. In a simple cubic quasi-free electron

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Number of conduction electrons in a Fermi sphere of known radius. In a simple cubic quasi-free electron metal, the spherical Fermi surface just touches the first Brillouin zone. Calculate the number of conduction electrons per atom in this metal as a function of the Fermi-Dirac integral. Consider the energy at the bottom of the conduction band to be EC = 0 eV.

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