In an ionic crystalline solid, atoms of element $Y$ forms hep structure. The atoms of element $X$ occupy one…
In an ionic crystalline solid, atoms of element $Y$ forms hep structure. The atoms of element $X$ occupy one third of tetrahedral voids. What is the formula of compound?
$\mathrm{X}_2 \mathrm{Y}_3$
$X Y$
$\mathrm{X}_3 \mathrm{Y}_3$
$\mathrm{XY}_2$
Solution
The atoms of element $\mathrm{Y}$ form hcp structure. The number of tetrahedral voids generated is twice the number of $\mathrm{Y}$ atoms. Thus, number of tetrahedral voids $=2 \mathrm{Y}$ The atoms of element $X$ occupy (1/3) of these tetrahedral voids.
Hence, number of $\mathrm{X}$ atoms $=2 \mathrm{Y} \times 1 / 3=2 / 3 \mathrm{Y}$ Ratio of $\mathrm{X}$ and $\mathrm{Y}$ atoms $=2 / 3 \mathrm{Y}: 1 \mathrm{Y}$ $=2 / 3: 1=2: 3$
$\therefore \quad$ Formula of compound $=\mathrm{X}_2 \mathrm{Y}_3$