In the mineral, spinel, having the formula ` MgAl_(2)O_(4)` oxide ions ar arranged , in the cubic close packing, ` Mg^(2+)` ions occupy the tetrahedrel voids while `Al^(3+)` ions occupy the octahedral voids.
(i) What precnetage of tetrahedral voids is occupied by ` Mg^(2+) ` ions ?
(ii) What precentage of octahedral voids is occupied by ` Al^(3+)` ions ?

Explanation

According to the formula `MgAl_2O_4`, if there are 4 oxide ions, there will be `1 Mg^(2+)` ion and `2 Al^(3+)` ions. But if the `4 O^(2-)` ions are in ccp arrangement, there will be 4 octahedral voids and 8 tetrahedral voids. Thus, `1 Mg^(2+)` ions is present in one of 8 tetrahedral voids
`therefore` % of tetrahedral voids occupied by `Mg^(2+)=1/8xx100=12.5%`
Similarly, `2 Al^(3+)` ions are present in two octahedral voids out of 4 available
`therefore` % of octahedral voids occupied by `Al^(3+) =2/4xx100=50%`