A solid `A^(o+)B^(ɵ)` has `NaCl`-type close-packed structure. If the anion has a radius of `250` pm, what should be the ideal radius for the cation? Can a cation `C^(o+)` having radius of `180` pm be slipped into the tetrahedral site of the crystal `A^(o+)B^(ɵ)`? Give reason for your answer.

Explanation

As `A^(+)B^(-)` has NaCI structure, `A^(+)` ions will be present in the octahedral voids. Ideal radius of the cation will be equal to the radius of the octahedral void because in that case it will touch the anions and the arrangement will be close packed. Hence
Radius of the octahedral void `=r_(A^+)=0.414xxr_(B^-)=0.414xx250=103.4"pm"`
Radius of the tetrahedral site `=0.225xxr_(B^-)=0.225xx250"pm"=56.25"pm"`
As the radius of the cation `C^(+)` (180pm) is larger than the size of the tetrahedral site, it cannot be slipped into it.