A compound is formed by two elements $A$ and B. The atoms of element B form ccp structure. The atoms of A…
A compound is formed by two elements $A$ and
B. The atoms of element B form ccp structure.
The atoms of A occupy $\frac{1}{3}$ of tetrahedral voids.
What is the formula of the compound?
$\mathrm{A}_2 \mathrm{~B}_3$
AB
$\mathrm{AB}_2$
$\quad \mathrm{AB}_3$
Solution
The atoms of element B form ccp structure. The number of tetrahedral voids generated is twice the number of B atoms. Thus, number of tetrahedral voids $=2 \mathrm{~B}$
$\begin{aligned} & \text { The atoms of element } A \text { occupy }(1 / 3) \text { of these } \\ & \text { tetrahedral voids. } \\ & \text { Hence, number of } A \text { atoms }=2 B \times 1 / 3=2 / 3 B \\ & \text { Ratio of } A \text { and } B \text { atoms }=2 / 3 \mathrm{~B}: 1 \mathrm{~B} \\ & =2 / 3: 1=2: 3 \\ & \therefore \quad \text { Formula of compound }=\mathrm{A}_2 \mathrm{~B}_3\end{aligned}$