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`, there are 4 oxide ions, `1 Mg^(2+)` and `2Al^(3+)` ions per formula unit. If 4 oxide ions are in ccp arrangment, there will be 4 octahedral voids and 8 terahedral voids. Thus, `1 Mg^(2+)` ion is present in one of the 8 tetrahedral voids and `2Al^(3+)` ions are present in 2 octahedral voids out of 4 available.
(i) Percentage of tetrahedral voids occupied by `Mg^(2+)` ion `= 1/8 xx 100 = 12.5 %`
(ii) Percentage of octahedral voids occupied by `Al^(3+)` ion
`= 2/4 xx 100 = 50%`.