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 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)/(sqrt2)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))`