Question

In face centre cubic unit cell, edge length is:

• A. $\frac{4}{\sqrt{3}}r$
• B. $\frac{4}{\sqrt{2}}r$
• C. $2r$
• D. $\frac{\sqrt{3}}{2}r$

Answer 1

The correct option is B $\frac{4}{\sqrt{2}}r$

Since the atoms are in contact on face diagonal.

So, length of diagonal = $r+2r+r$ = $4r$.

$AC$ = $4r$.

In right $△ABC$,

${AC}^2={AB}^2+{BC}^2$

${\left(4r\right)}^2=a^2+a^2$

On solving this equation, we get -

$a=\frac{4}{\sqrt{2}}r$.

Hence, the correct answer is option $\text{B}$.