Question

In the structure of a compound, oxide ions are cubic close packed whereas $\frac{1}{8}th$ of tetrahedral voids are occupied by $A^{2+}$ cation and half of octahedral voids are occupied by $B^{3+}$ cations. The general formula of the compound having structure is:

• A. $AB{O}_2$
• B. $A{B}_2{O}_4$
• C. $A{B}_{2}O$
• D. $A_{2}BO$

Answer 1

The correct option is B $A{B}_2{O}_4$

Effective number of $O^{2-}$ ion in a unit cell
$=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
Effective number of $A^{2+}$ in a unit cell $=8\times \frac{1}{8}=1$
Effective number of $B^{3+}$ in a unit cell $=4\times \frac{1}{2}=2$
$\therefore$ General formula is $A{B}_2{O}_4$.