If `'a'` stands for the edge length of the cubic systems: simple cubic,body centred cubic and face centred cubic then the ratio of radii of the spheres inthese systems will be respectively,

Options

A. `1/2 a : (sqrt3)/(4) a : (1)/(2 sqrt2) a `
B. `1/2 a: sqrt3 a : (1)/(sqrt2) a `
C. `1/2a: (sqrt3)/(2) a : (sqrt3)/(2) a `
D. `1a: sqrt3a : sqrt2a`

Answer

A

Explanation

If a=edge length of cubic systems, then for simple cubic structure, radius=a/2
For body centred cubic structure, radius = `(sqrt3)/(4) a`
For face centred cubic structure, radius ` = (a)/(2sqrt2)`
Hence, the ratio of radii `1/2 a: (sqrt3)/(4) a : (1)/(2 sqrt2) a `