Question

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ${}^{\prime }{a}^{\prime }$, the closest approach between two atoms in metallic crystal will be:

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

Answer 1

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

In FCC, one of the face is like as shown in figure:
By pythagoras theorem in $\Delta ABC$,
$2a^2=16r^2$
$\Rightarrow r^2=\frac{1}{8}{a}^2$
$\Rightarrow r=\frac{1}{2\sqrt{2}}a$
Distance of closest approach, $\Rightarrow 2r=\frac{a}{\sqrt{2}}$