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

Answer

d

Explanation

For simple cabic `r = (a)/(2)`
For bcc ` r = (sqrt(3)a)/(4)`
For fcc `r = (a)/(2sqrt(2))`
`So sc: bcc:fcc`
`(a)/(2) :( sqrt(3)a)/(2) : (a)/(2 sqrt(2))`