 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/65/a/solution

A face-centered cubic cell has atoms at its corners and face centers. The

(111)

plane intercepts the three positive cubic axes at

(a_{0}, 0, 0)

(0, a_{0}, 0)

and

(0, 0, a_{0})

; it is a close-packed triangular layer. Close-packed directions are the

⟨ 110 ⟩

family, with the in-plane members satisfying

u + v + w = 0

Nearest neighbors touch along a face diagonal:

4 r = 2 a_{0}

. Hence

r = \frac{a _{0}}{2 2} = 1.389 \overset{˚}{A} .

The body diagonal is not the touching direction for this crystal structure.

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