A one-dimensional row of ions has spacing .

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 Electrons in a periodic potential: Bloch's theorem and the opening of a gap

Problem

A one-dimensional row of ions has spacing a=3.2 A˚a = 3.2\ \mathrm{\mathring{A}}. ((a)) Using Bragg's law at normal incidence, show that the first zone boundary sits at k=π/ak = \pi/a, and find its numerical value. ((b)) Find the energy a free electron would carry at that wavevector, using ℏ2/2m=3.81 eV A˚2\hbar^2/2m = 3.81\ \mathrm{eV\,\mathring{A}^2}.

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