 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/34e/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Using

b_{i} = 2 π (a_{j} \times a_{k}) / V

gives

b_{1} = (2 π / a) (0, 1, 1)

b_{2} = (2 π / a) (1, 0, 1)

b_{3} = (2 π / a) (1, 1, 0)

. The reciprocal cell volume is

(2 π)^{3} / V = 16 π^{3} / a^{3}

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