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ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-3/section-d/43/b/v/solution

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Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section D / 43 / b / v / Solution by

Codex  0 2026-10-20

At fixed number density, attempt frequency, nearest-neighbour distance and barrier, the conductivities have ratio $σ_{sc} : σ_{bcc} : σ_{fcc} = 1 : 4/3 : 2$ . Thus the face-centred cubic array is largest. Numerically,

F = 1 0^{13} exp [- \frac{0.35}{( 8.61733 \times 1 0 ^{- 5} ) ( 300 )}] ≃ 1.32 \times 1 0^{7} s^{- 1},

(1)

σ_{fcc} = \frac{2 n Q ^{2} F a ^{2}}{k _{B} T} ≃ 1.47 \times 1 0^{- 7} S m^{- 1} .

(2)

The small value is consistent with the low supplied carrier number density and strongly activated hopping. This comparison holds

n

fixed rather than comparing fully occupied crystal structures, whose site densities at the same neighbour distance differ.

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