Question

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

विकल्प

• `sqrt 2 a`

• `a/sqrt 2`

• 2a

• `2 sqrt 2 a`

Answer 1

A metal crystallises in a face-centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be `bbunderline(a/sqrt 2)`.

Explanation:

In a face-centred cubic (FCC) structure:

Atoms touch each other along the face diagonal of the cube.

Face diagonal = `sqrt 2 a`

Along this diagonal, two atoms touch each other, meaning Closest distance (or closest approach) = `"Face diagonal"/2`

= `(sqrt 2 * a)/2`

= `a/sqrt 2`

∴ The closest approach between two atoms in metallic crystal will be `a/sqrt 2`.