1.

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 :

Answer»

`(1)/(2)a : ( sqrt(3))/( 4) a : ( 1)/( 2 sqrt(2)) a`
`(1)/(2)a :sqrt(3) a : ( 1)/(sqrt(2)) a`
`(1)/(2)a : ( sqrt(3))/( 2) a : ( sqrt(2))/( 2) a `
`1a : sqrt(3) a : sqrt(2) a `

Solution :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 `


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