Question

Percentage of empty space in body centered cubic unit cell is nearly:

• A. $52.36$
• B. $68$
• C. $32$
• D. $26$

Answer 1

The correct option is C $32$

In body centered cubic unit cell, $z=2$ and
$\sqrt{3}a=4r$
$P.F.=\frac{2\times \frac{4}{3}\pi r^3}{a^3}$
$P.F.=\frac{2\times \frac{4}{3}\pi r^3}{64r^3}\times 3\sqrt{3}$
$P.F.=68\%$
And hence empty space = $32\%$