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ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2023/paper-2/a9/a/iii/solution

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Past exam of the chemistry A course of the University of Cambridge / 2023 / Paper 2 / A9 / a / iii / Solution by

Codex  0 2026-10-20

Using the printed

x, y

axes, take a lower vertex of cell B as origin. One allowed pair of primitive lattice translation vectors is

a_{1} = a (\hat{x} + \hat{y}), a_{2} = a (- \hat{x} + \hat{y}) .

(1)

Both vectors connect nearest lattice points, have length

2 a

, and are perpendicular. Their determinant has magnitude

2 a^{2}

, consistent with a primitive area. Exchanging them or reversing their directions gives equivalent basis conventions; the corresponding reciprocal lattice vectors must then use the same convention.

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