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 ?

Options

A. 0.5
B. 0.25
C. 0.75
D. `12.5%`

Answer

D

Explanation

In a cubic close packed lattice of oxide ions, there would be two tetrahedral and one octahedral void per oxide ion.
Since the formula shows the presenece of 4 oxide ions, the number of tetrahedral voids is eight and that of octahedral voids is four .
Out of the eight tetrahedral voids one is occupied by A.
`:.` Percentage of tetrahedral voids occupied
`=(1)/(8)xx100=12.5%`