Question

The structure of a mixed oxide is cubic close packed (ccp). 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 B

$A_{2}B{O}_2$

Number of atoms in $CCP=4\Rightarrow O^{2-}$
No. of tetrahedral voids $=2\times N=2\times 4=8$
No. of $A^{2+}ions=8\times \frac{1}{4}=2$
No. of octahedral voids = N = 4
No. of $B^{+}ions=4$
Ratio $\Rightarrow O^{2-}:A^{2+}:B^{+}\Rightarrow 4:2:4\Rightarrow 2:1:2$
Formula $\Rightarrow A{B}_2{O}_2$