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A metal has a face-centred cubic lattice. If the unit cell edge length is denoted by a, what is the minimum distance between two neighbouring atoms in the crystal?

1. 2a
2. 2√2a
3. √2a
4. a/√2

Correct answer: a/√2

Solution

In a face-centered cubic (FCC) lattice, the atoms are located at the corners and the centers of each face of the cube. The minimum distance between neighboring atoms occurs along the face diagonal, which can be calculated as the distance from one corner atom to the center atom on the face, resulting in a distance of a/√2.

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