If `a ` stands for the edge length of the cubic system `:` simple cubic, body `-` centred cubic anf face `-` centred cubic, then the ratio of radii of the spheres in these systems will be respectively`:`

Options

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

Answer

c

Explanation

For simple cubic,
`(r^(+))/(r^(-))=(a)/(2) (` where `a` is edge length `)`
For `b.c.c.,(r^(+))/(r^(-))=(asqrt(3))/(4)`
For `b.c.c.,(r^(+))/(r^(-))=(a)/(2sqrt(2))`