Determine the ratio of radii of particles in simple, body-centred and face-centred cubic unit cells. Assume the edge length of each type of unit cell is a.

Explanation

Suppose, the radii of constituent particles in simple, body-centred and face-centred cubic unit cell are `r_(1),r_(2)andr_(3)` respectively.
The relations between the radii of particles and the edge lengths of different unit cells are given below:
Simple cubic unit cell: `r_(1)=a/2`, BOdy-centred unit cell `r_(2)=sqrt3/4a`, Face-centred cubic unit cell : `r_(3)=a/(2sqrt2)`
`thereforer_(1):r_(2):r_(3)=a/2:sqrt3/4a:a/(2sqrt2)`
`=1:sqrt3/2:1/sqrt2=1:1.732:0.707`