Question

If the radius of an atom of an element is $75$ pm and the lattice is body-centred cubic, the edge of the unit cell will be :

• A. $32.475$ $pm$
• B. $173.2$ $pm$
• C. $37.5$ $pm$
• D. $212.1$ $pm$

Answer 1

The correct option is B $173.2$ $pm$

For body centered cubic lattice, the relationship between the edge length a and the radius r is as given below:

$a=\frac{4r}{\sqrt{3}}$

Substituting values in the above expression, we get

$a=\frac{4\times 75}{\sqrt{3}}=173.2$ pm

Hence, the edge length of the unit cell is $173.2$ pm.