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

Answer

C

Explanation

Simple cubic unit cell, `r=a//2`
Body-centred cubic unit cell, `r=(asqrt(3))/(4)`
Face-centred cubic unit cell, `r-(a)/(2sqrt(2))`