Question

A metal crystallizes in a face centered cubic structure. If the edge length of its unit cell is ‘$a$’, the closest approach between two atoms in metallic crystal will be:

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

Answer 1

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

Let's suppose a fcc arrangement of atoms, having edge length $a$ and radius of atoms as $r$.

For fcc arrangement, $4r=\sqrt{2}a$
(where $\sqrt{2}a$ is the diagonal of the cubic face )
$\therefore$ Closest distance = 2r = $\frac{\sqrt{2}a}{2}$ = $\frac{a}{\sqrt{2}}$