Question

A compound is formed by elements of $X,Y$ and $Z$. Atoms of $Z$ (anions) make fcc lattice. Atoms of $X$ (cations) occupy all the octahedral voids. Atoms of $Y$ (cations) occupy $\frac{1}{3}$ rd of the tetrahedral voids. The formula of the compound is

• A. $X_3{Y}_2{Z}_3$
• B. $X_{2}YZ$
• C. $X{Y}_{2}Z$
• D. $X_2{Y}_{2}Z$

Answer 1

Answer: (A)

Since, $Z$ forms fcc lattice so per unit cell number of $Z$ atoms $=4$

In fcc structure total number of octahedral voids $=4=$ number of $X$ atoms.

In fcc structure, total number of tetrahedral voids $=8$

Thus, number of $Y$ atoms $=\frac{1}{3}\times 8=\frac{8}{3}$

Thus, formula of compound is $Z_4{X}_4{Y}_{8/3}$ or $X_4{Y}_{8/3}{Z}_4$ or $X{Y}_{2/3}Z$ or $X_3{Y}_2{Z}_3$