Question

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:

• A. $2\sqrt{2}a$
• B. $\sqrt{2}a$
• C. $\frac{a}{\sqrt{2}}$
• D. $2a$

Answer 1

The correct option is C $\frac{a}{\sqrt{2}}$

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
$\frac{1}{2}\times \text{length of face diagonal}$....(1)

But
$\text{length of face diagonal}=\sqrt{2}a$ ....(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

$\frac{1}{2}\times \sqrt{2}a=\frac{a}{\sqrt{2}}$

Hence, the option (C) is the correct answer.