If `a` stand for the edge length of the cube system simple cubic , body centred cubes and face centred cubic ,then the ratio of radii of the sphares in these system will be respectively

Options

A. `(1)/(2) a: sqrt(3)/(2)a: sqrt(2)/(2) a`
B. `1a: sqrt(3a) : sqrt(2a)`
C. `(1)/(2) a: sqrt(3)/(4)a: (1)/(2sqrt(2)a`
D. `(1)/(2)a: sqrt(3a) : (1)/(sqrt(2) a`

Answer

c

Explanation

`{:(Sc,2r=a,implies,r=a//2),(bc c,4r=sqrt(3)a,implies,r=(sqrt(3)xxa)/(4)),(fc c,4r=sqrt(2)a,implies,r=a/(2sqrt(2))):}`