Question

A mixed oxide crystallizes in a cubic unit cell. Oxide ions are present in a ccp arrangement. Half of the tetrahedral voids are occupied by monovalent metal '$A$' and the octahedral voids are fully occupied by a monovalent metal '$B$'. The formula of the oxide is:

• A. $A{B}_2{O}_3$
• B. $A_2{B}_3{O}_3$
• C. $A{B}_3{O}_2$
• D. $ABO$

Answer 1

The correct option is D $ABO$

The number of $O^{2-}$ ions in cubic close packing $=n$
$\therefore$ Number of octahedral voids $=n$
Number of tetrahedral voids $=2n$
Divalent metal ions '$A$' present $=\frac{1}{2}\times 2n=\frac{2n}{2}=n$
Monovalent metal ions '$B$' present $=n$
$\therefore$ Ratio $A:B:O^{2-}$
$=n:n:n$
$=1:1:1$

Hence, the formula would be $=ABO$