Chemistry - Solid State Question with Solution | TestHub

Following generalization can be easily derived for various types of lattice arrangements in cubic cells between the edge length $(a)$ of the cell and $r$ the radius of the sphere. For simple cubic: $a=2r$ or $r=\frac{a}{2}$ For body centred cubic : $$a=\frac{4}{\sqrt{3}}r\text{ or }r=\frac{\sqrt{3}}{4}a$$ For face centred cubic : $$a=2\sqrt{2}r\text{ or }r=\frac{1}{2\sqrt{2}}\mathrm{a}$$ Thus the ratio of radii of spheres for these will be simple $:\mathrm{bcc}:\mathrm{fcc}$ $=\frac{a}{2}:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$ i.e. option (a) is correct answer.