If 'a' stands for the edge length of the cubic system `:` simple cubic , body centred cubic and face centred cubic, then the ration of the radii of the spheres in these systems will be respectively `:`

Options

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

Answer

A

Explanation

For simple cubic, `a = 2r :. R = ( a)/( 2)`
for bcc, `4r = sqrt( 3) a :.r= ( sqrt(3)a)/( 4)`
for fcc, `4r = sqrt(2)a :.r=(sqrt(2)a)/(4)`
Ration is `: ( a)/(2) : ( sqrt(3)a)/( 4) : ( sqrt( 2) a )/( 4)`
or `( 1)/(2) a : ( sqrt( 3) )/(4) a : ( 1)/( 2 sqrt( 2)) a `