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 :

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

Answer 1

Answer: (B)

$\frac{a}{\sqrt{2}}$

Answer 2

In FCC, one of the face is like

By $\Delta ABC$,

$2a^{2} = 16r^{2}$
$\Rightarrow r^{2} = \frac{1}{8} a^{2}$
$\Rightarrow r = \frac{1}{2 \sqrt{2}} a$

Distance of closest approach $= 2r = \frac{a}{\sqrt{2}}$