Question

In a face-centred cubic system, the distance d between the nearest neighbours is given by ______.

Options

• d = a

• `d = sqrt 2a`

• `d = (sqrt 3a)/2`

• `d = a/sqrt2`

Answer 1

In a face-centred cubic system, the distance d between the nearest neighbours is given by `bbunderline(d = a/sqrt2)`.

Explanation:

In a face-centred cubic (FCC) lattice:

Atoms touch each other along the face diagonal.

The length of the face diagonal = `sqrt 2 * a`

This diagonal contains 2 atomic radii (2r) between nearest neighbours

So, `2r = (sqrt2 * a)/1`

⇒ `r = a/(sqrt 2 * 2)`

r = `a/(2 sqrt 2)`

But the nearest neighbour distance (d) = 2r

d = `a/sqrt 2`