Question

A metal crystallises in bcc lattice. The percentage fraction of edge length not covered by the atom is:
(Given $\sqrt{3}=1.73$)

• A. 10.4 %
• B. 13.4 %
• C. 12.4 %
• D. 11.4 %

Answer 1

The correct option is B 13.4 %

In a bcc lattice, $r=\frac{\sqrt{3}a}{4}$

where, the edge length of a unit cell $=a$
the radius of the atom $=r$

Therefore, the edge length not covered by the atom = $a-2r$
$=a-\frac{\sqrt{3}a}{2}$
$=a\left[\frac{2-\sqrt{3}}{2}\right]$

The percentage fraction not covered,
$=\frac{a\left[\frac{2-\sqrt{3}}{2}\right]}{a}\times 100$
$=0.134\times 100$
$=13.4\%$