JEE Main 2023 — Solid State Question with Solution

A compound is formed by two elements $$\mathrm{X}$$ and $$\mathrm{Y}$$. The element $$\mathrm{Y}$$ forms a cubic close-packed (CCP) arrangement, and element $$\mathrm{X}$$ occupies one third of the tetrahedral voids.

In a CCP structure, there are 4 atoms of $$\mathrm{Y}$$ in a unit cell. This means there are 8 tetrahedral voids in the CCP structure.

Since $$\mathrm{X}$$ occupies one third of the tetrahedral voids, there are $$\frac{1}{3}\times 8=\frac{8}{3}$$ atoms of $$\mathrm{X}$$ in the formula unit.

The ratio of $$\mathrm{X}$$ to $$\mathrm{Y}$$ in the formula unit is $$\frac{8}{3}:4=\frac{2}{3}:1$$. Multiplying both parts of the ratio by 3, we get $$2:3$$.

So, the formula of the compound is $${\mathrm{X}}_2{\mathrm{Y}}_3$$