A metal crystallises in face centred cubic structure. If the edge of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be:

For face centred cubic structure, the closest approach between two atoms in metallic crystal will be equal to one half the length of the face diagonal. It will be
1/2 × length of face diagonal (1)
But length of face diagonal = √2a (2)
Here, a is the edge of its unit cell.
From (1) and (2), the closest approach between two atoms in metallic crystal will be
1/2 × √2a = a√2
Hence, the option (C) is the correct answer.