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)=CE^1/2, with C=4πV(2m_e/h²)^3/2. Show that at T=0,

and deduce that μ(0)=(3N/8π)^2/3(h²/2m_e), 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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f(E)=1 for E<μ f(E)=0 for E>μ