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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/57/d/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 57 / d / Solution by

Codex  0 2026-10-20

Write the ordinary structure factor as

F_{0} = ∣ F_{0} ∣ e^{i ϕ}

and use

F = F_{0} + 19.2 i

. The intensities imply

∣ F_{0} ∣ = 13130 = 114.59, 15430 = 13130 + 19. 2^{2} + 2 (19.2) ∣ F_{0} ∣ sin ϕ .

(1)

Consequently

sin ϕ = 0.43893

, and the two possible ordinary phases are

ϕ ≃ 26. 0^{\circ} or 154. 0^{\circ} .

(2)

The twofold ambiguity is expected from a single anomalous-intensity constraint. The calculation assumes that the specified imaginary increment is the only change requiring inclusion; an additional unspecified real dispersive change could not be reconstructed from these data alone.

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