Question

$Na$ and $Mg$ crystallize in bcc and fcc type crystals respectively. The number of ions of $Na$ and $Mg$ present in the unit cell of their respective crystal is:

• A. $4\text{and}2$
• B. $9\text{and}14$
• C. $14\text{and}9$
• D. $2\text{and}4$

Answer 1

The correct option is D $2\text{and}4$

In BCC

There are $8$ atoms on corner and one in body center.
Corner atom with contribution $\left(1/8\right)$
So, $1\times 1+\frac{1}{8}\times 8=2$.
In FCC

$6$ atoms are on face center with contribution $\frac{1}{2}$, eight atom on corner.
$8\times \frac{1}{8}+\frac{1}{2}\times 6=4$