Potassium is body-centred cubic with

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

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

Problem

Potassium is body-centred cubic with a=5.225 A˚a=5.225\,\mathrm{\mathring{A}}, two atoms per conventional cell, monovalent. A Hall-bar sample of potassium carries a current I=12 AI=12\,\mathrm{A} along xx in a field Bz=0.60 TB_z=0.60\,\mathrm{T}; the bar is d=1.5 mmd=1.5\,\mathrm{mm} thick along zz, the field direction, and a transverse Hall voltage VH=−2.14 μVV_H=-2.14\,\mu\mathrm{V} develops. ((a)) Find the Hall coefficient RH=VHd/(IBz)R_H=V_Hd/(IB_z) and the carrier density it implies. ((b)) Compare that carrier density with the value predicted from potassium's structure and valence, and comment.

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