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

Answer

A

Explanation

If a = edge length of cubic systems
`" For simple cubic structure, radius"=(a)/(2)`
`"For body centred cubic structure, radius"=(sqrt3)/(4)a`
`"For face centred cubic structure, radius"=(a)/(2sqrt2)`
`"Hence, the ratio of radii"=(1)/(2)a:(sqrt3)/(4)a:(1)/(2sqrt2)a`