Question

In an atomic bcc, what fraction of edge (in percentage) is not covered by atoms?

Answer 1

In body centre cubic unit cell atoms are present at corner + Body centre
Edge length = a

In bcc $\sqrt{3}a=4r\Rightarrow r=\frac{\sqrt{3}}{4}\times a$
So; edge not covered $=a-2r$
$=a-2\times \frac{\sqrt{3}}{4}\times a$
$=a(1-\frac{\sqrt{3}}{2})$

Fraction of edge is not covered by $=\frac{a(1-\frac{\sqrt{3}}{2})}{a}\times 100=13.4\text{\%}$