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_(2)O_(4)` , if there are 4 oxide ions, there will be ` 1 Mg^(2+)` ions and `2Al^(3+) ` ions. But if the ` 4O^(2-)` ions are in cp arrangement, there will be 4 octahedral voids and 8 tetrahedral voids. Thus ` 1 Mg^(2+)` ions is presnet in one of the 8 tetrahedral voids.
%e of tetrahedral voids occupied by ` Mg^(2+) = 1/8 xx 100 = 12.5%`
Similarly ` 2Al^(3+)` ions are presnet in two octahedral voids out of 4 available .
% of octahedral voids occupied by ` Al^(3+) = 2/4 xx 100 xx 50 %`