Potassium is a free-electron metal of density and molar mass

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Dielectric and optical properties of solids · Dielectric and optical properties of solids

Solid State Physics, Ch Collective and coupled excitations: plasmons, polaritons and polarons

Problem

Potassium is a free-electron metal of density 0.862 g cm−30.862\,\mathrm{g\,cm^{-3}} and molar mass 39.10 g mol−139.10\,\mathrm{g\,mol^{-1}}, with one conduction electron per atom. Treat the background permittivity as εb=1\varepsilon_b=1 (a bare free-electron metal). ((a)) Calculate the free-electron density nn and the unscreened plasma energy ℏωp\hbar\omega_p. ((b)) Give the corresponding wavelength λp=hc/ℏωp\lambda_p=hc/\hbar\omega_p and state, in one sentence, for which wavelengths potassium should reflect and for which it should transmit.

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