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

The Correct Option is C

$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 $