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/(2sqrt(2)) a`
B. `1/2 a : sqrt(3) a : 1/(sqrt(2)) a`
C. `1/2 a : (sqrt3)/2 a : (sqrt2)/(2) a`
D. `1a : sqrt(3) a : sqrt(2) a`

Answer

A

Explanation

For simple cubic , `a = 2r " " :. " " r = a/2`
For bcc, `" " 4r = sqrt(2)a " " :. " " r = (sqrt(3)a)/(4)`
For fcc, `" " 4r = sqrt(2)a " " :. " " r = (sqrt(2)a)/(4)`
Ratio is : `a/2 : (sqrt(3)a)/(4) : (sqrt(2)a)/(4)`
or `1/2 a : (sqrt3)/(4)a : 1/(2sqrt(2))a`.