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 : sqrt3/2 a : sqrt2/2 a`
B. `1a : sqrt3a : sqrt2a`
C. `1/2 a : sqrt3/4 a : 1/(2sqrt2)a`
D. `1/2a : sqrt3a : 1/sqrt2 a`

Answer

C

Explanation

For simple cubic :`r = a//2`
For body-centred : `r=asqrt3//4`
where a = edge length, r = radius
For face-centred : `r= a/(2sqrt2)`
`:.` Ratio of radii of the three will be
`a/2 : (asqrt3)/4 : a/(2sqrt2)`