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. $X_{2} Y Z$
• 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 $X_{3} Y_{2} Z_{3}$