Zinc has mass density

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The free-electron gas: what Drude gets right and what only Fermi fixes

Problem

Zinc has mass density ρ=7140 kg m−3\rho=7140\,\mathrm{kg\,m^{-3}}, molar mass Mmol=65.38 g mol−1M_{\rm mol}=65.38\,\mathrm{g\,mol^{-1}}, and gives up two conduction electrons per atom. ((a)) Find its conduction electron density nn. ((b)) Find its Fermi energy EFE_F. ((c)) Predict its electronic heat capacity coefficient γ\gamma; for ZvZ_v electrons per atom the formula of Section 8.7 generalises to γ=π2RZv/2TF\gamma=\pi^2RZ_v/2T_F. Zinc's measured γ\gamma is 0.97 mJ mol−1K−20.97\,\mathrm{mJ\,mol^{-1}K^{-2}}: by what factor does the measurement exceed the free-electron prediction?

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