Question

A given metal crystallizes out with a cubic structure having edge length of $361pm$. If there are four metal atoms in one unit cell, what is the radius of one atom?
(AIPMT 2015)

• A. $80pm$
• B. $108pm$
• C. $127pm$
• D. $40pm$

Answer 1

The correct option is C $127pm$

There are four atoms per unit cell, hence, it is of face centred cubic lattice.

In fcc structure, atoms are touching along the face diagonal.
If 'a' is the edge length of the cell then, the face diagonal is $\sqrt{2}a$.

$\therefore 2r=\frac{\sqrt{2}a}{2}$
$r=\frac{a}{2\sqrt{2}}=\frac{361}{2\times 1.414}\approx 127pm$

Hence, option (a) is correct.