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An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

1. a
2. √2 a
3. a/√2
4. a/2

Correct answer: a/√2

Solution

In an fcc lattice the octahedral voids lie at the body centre (1/2,1/2,1/2) and at the 12 edge centres. The nearest pair, e.g. body centre to an edge centre, are separated by sqrt((a/2)^2 + (a/2)^2) = a/sqrt(2).

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