In a crystalline solid, having formula `AB_(2)O_(4)` oxide ions are arranged in cubic close packed lattice while cations A are present in tetrahedral voids and cations B are present in octahedral voids.
(a) What percentage of the tetrahedral voids is occupied by A?
(b) What percentage of the octahedral voids is occupied by B ?

Answer

`A=12.5%, B=50%`

Explanation

In cubic close packed lattice of oxide ions there would be two tetrahedral voids and one octahedral void for each oxide ion.
`therefore` For four oxide ion, there would be 8 tetrahedral voids and 4 octahedral voids. Out of these, 2 are occupied by B.
Percentage of tetrahedral voids occupied by A = `1//8xx100=12.5%`
Percentage of octahedral voids occupied by B. `=2//4xx100=50%`.