Question

A metal crystallises in bcc lattice. The percentage of edge length not covered by atom is :

• A. 25.6%
• B. 13.4%
• C. 10.4%
• D. 15.5%

Answer 1

The correct option is B 13.4%

In a bcc lattice, atoms are present at corners and at body centre
In bcc,
$r=\frac{\sqrt{3}a}{4}$
here r is the radius of atom and a is the edge length.


As shown :
$\text{Edge length not covered by atom}=a-2r$

$\Rightarrow a-\frac{\sqrt{3}\times a}{2}=\frac{(2-\sqrt{3})\times a}{2}$


$\therefore \text{Percentage edge length not covered}=\frac{\frac{(2-\sqrt{3})\times a}{2}}{a}\times 100\%=\frac{2-1.732}{2}\times 100\%=13.4\%$