In a simple, body-centred and face-centred cubic unit cell, the radii of constituent particles are `r_(1),r_(2)andr_(3)`, respectively. If the edge length of each type of these unit cells be a, then find the ratio of `r_(1),r_(2)andr_(3)`.

Explanation

For the cubic unit cell, `r_(1)=a/2,r_(2)=(sqrt3a)/4,r_(3)=a/(2sqrt2)`
`thereforer_(1):r_(2):r_(3)=a/2:(sqrt3a)/4:a/(2sqrt2)=2:sqrt3:sqrt2`