`Br^(-)` ions form close packed structure. If the radius of `Br^(-)` ion is 195 p, calculate the radius of the cation that just fits in the tetrahedral hole. Can a cation `A^(+)` having a radius of 82 pm be slipped into the octahedral hole of the crystal `A^(+) Br^(-)`?

Explanation

Radius of cation just fitting into tetrahedral hole = Radius of tetrahedral hole
`=0.225xxr_(Br^-)`
=0.225 x 195 = 43.875 pm
Radius ratio `(r^(+)/r^(-))=82/195`=0.4205
This radius ratio lies in the range 0.414-0.732 hence, cation can slip into octahedral hole.