Question

In a compound, $X{Y}_2{O}_4$, oxide ions are arranged in ccp and cations $X$ are present in octahedral voids. Cations $Y$ are equally distributed among octahedral and tetrahedral voids. The fraction of the octahedral voids occupied is:

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{6}$
• D. $\frac{1}{8}$

Answer 1

The correct option is B $\frac{1}{2}$

No of atoms in ccp is $4$ and in this question these are oxide ions. So there will be $8$ tetrahedral voids and $4$ octahedral voids per unit cell. In a unit cell $1X$ and $1Y$ occupy octahedral voids. So $2$ out of $4$ octahedral voids are occupied which implies $50\%$ or $\frac{1}{2}$ is the fraction of octahedral voids occupices. So, correct answer is option A.