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 inthese systems will be respectively,

Options

A. `(1)/(2)a:(sqrt3)/(2)a:(sqrt2)/(2)a`
B. `1a:ssqrt(3a):sqrt(2a)`
C. `(1)/(2)a:(sqrt3)/(4)a:(1)/(2sqrt2)a`
D. `(1)/(2)a:sqrt3a:(1)/(sqrt2)a`

Answer

C

Explanation

For simle cubic :
`r^(+)//r^(-)=(a)/(2)`
Here a = edge length and
`r^(+)//r^(-)`= interatomic distance
For body centered :
`r^(+)//r^(-)=(asqrt3)/(4)`
For face centered :
`r^(+)//r^(-)=(a)/(2sqrt2)`
Therefore ratio of radii of the three will be
`(a)/(2):(asqrt3)/(4):(a)/(2sqrt2)`