Potassium metal has one conduction electron per atom

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

Solid State Physics, Ch The degenerate electron gas, finished

Problem

Potassium metal has one conduction electron per atom, electron density

n=1.40\times10^{28}\,\mathrm{m^{-3}}

and Fermi energy

E_F=2.12\,\mathrm{eV}

. Its measured bulk modulus is

2.81\,\mathrm{GPa}

. ((a)) Estimate the

T=0

degeneracy pressure of the conduction electrons,

P=\tfrac25nE_F

. ((b)) Estimate the corresponding degeneracy bulk modulus

B=\tfrac23nE_F

. ((c)) Compare the estimate with the measured bulk modulus, quoting the ratio, and comment on what the comparison shows for an alkali metal.

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