Question

The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is : (Edge length is represented by 'a') :

• A. 0.134 a
• B. 0.027 a
• C. 0.067 a
• D. 0.047 a

Answer 1

Answer: (C)

0.067 a

Answer 2

$a = 2\left(R + r\right)$
$\frac{a}{2} =\left(R+r\right)$ .....(1)

$a\sqrt{3} =4R$ .....(2)

Using (1) & (2)

$\frac{a}{2} = \frac{a\sqrt{3}}{4} =r$
$a\left(\frac{2-\sqrt{3}}{4}\right)=r$
$r=0.067\, a$