Apply the free-electron model to two more solids

PHYSICS · Subjective · 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

Apply the free-electron model to two more solids. (a) Magnesium has mass density 1738 kg m−31738\,\mathrm{kg\,m^{-3}}, molar mass 24.305 g mol−124.305\,\mathrm{g\,mol^{-1}}, and gives up two conduction electrons per atom. Find its electron density nn and, using the generalised formula γ=π2RZv/2TF\gamma=\pi^2RZ_v/2T_F, its predicted electronic heat capacity coefficient γ\gamma and its predicted Hall coefficient RH=−1/neR_H=-1/ne. Magnesium's measured values are γ=1.30 mJ mol−1K−2\gamma=1.30\,\mathrm{mJ\,mol^{-1}K^{-2}} and RH=−0.83×10−10 m3 C−1R_H=-0.83\times10^{-10}\,\mathrm{m^3\,C^{-1}}: how well does the model do? (b) Diamond has n=7.05×1029 m−3n=7.05\times10^{29}\,\mathrm{m^{-3}} (Section 8.10) with four conduction electrons per atom. Predict its electronic heat capacity coefficient by the same formula. Diamond is one of the best electrical insulators known, with no measurable linear-in-TT electronic heat capacity at all. (c) In one or two sentences, say why magnesium's result and diamond's result are two different kinds of disagreement with measurement.

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