Question

Structure of a is mixed oxide is cubic close packed (cpp). The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal $A$ and the octahedral voids are occupied by a monovalent metal $B$. The formula of the oxide is

• A. $AB{O}_2$
• B. $A_{2}B{O}_2$
• C. $A_2{B}_3{O}_4$
• D. $A{B}_2{O}_2$

Answer 1

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

Number of atoms in cpp = $4$
So, number of $O^{2-}$ ion = $4$
Number of tetrahedral voids = $2\times 4$
Number of $A^{2+}$ ions = $8\times \frac{1}{4}=2$
Number of octahedral voids =
Number of $B^{+}$ ions = $4$
Ratio, $O^{2-}:A^{2+}:B^{+}=4:2:4=2:1:2$
Formula of the oxide = $A{B}_2{O}_2$