In this and the following problem we explore further some of the properties of the FermiDirac distribution,

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In this and the following problem we explore further some of the properties of the Fermi–Dirac distribution, eqn 18C.6. For a threedimensional solid of volume V, it turns out that ρ(E)=CE1/2, with C=4πV(2me/h2)3/2. Show that at T=0,

and deduce that μ(0)=(3N/8π)2/3(h2/2me), where N=N/V, the number density of electrons in the solid. Evaluate μ(0) for sodium (where each atom contributes one electron).

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