`LiI` occurs as cubical closed packing. If the edge lenth of unit cell is `624` pm, determine the ionic radii of `Li^(o+)` and `I^(Θ)` inos.

Explanation

The cubical closed packing has a face-centred cubic unit cell. `I^(Θ)` occupy the corners and the face centres. These ions touch each other along the face diagonal of the cube.
Hence
`4r_(I^(Θ)) = sqrt2a`
`r_(I^(Θ)) = (a)/(sqrt2a)= (624 "pm")/(2(1.414))= 220.65` pm
Now along the edge , we will have `I^(Θ) Li^(o+) I^(Θ)` arrangement, where `I^(Θ)` ions are at the corners and `Li^(o+)` ions at the centre of the edge (octahedral void). Since in cloest packing they touch each other, we will have
`2r_(I^(Θ)) + 2r_(Li^(o+)) = a`
or `r_(Li^(o+))= (a)/(2) - r_(I^(Θ)) = (624 "pm")/(2) - 220.65 pm = 91.35` pm