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’)

Regarding bcc structure: $\sqrt{3}a=4r\Rightarrow r=\frac{\sqrt{3}a}{4}$
Space at the edge $=a-2r$

 Edge-to-edge void $=a-\frac{\sqrt{3}a}{2}$ = sphere's diameter
$r_{sphere}=\frac{a-\frac{\sqrt{3}}{2}a}{2}=\left(\frac{2-\sqrt{3}}{4}\right)a=0.067\mathrm{a}$

Therefore, the correct option is (C) 0.067 a.