Chemistry - Solid State Question with Solution | TestHub

Let the number of atoms of element Y forming the hexagonal close-packed (hcp) lattice be $N$.

The number of octahedral voids in a close-packed structure is equal to the number of atoms forming the lattice, which is $N$.

Since atoms of element X occupy $\frac{2}{3}$ of the octahedral voids, the number of atoms of X is $\frac{2}{3}N$.

The ratio of the number of atoms of X to that of Y is $\frac{2}{3}N:N=2:3$.

Thus, the formula of the compound is ${\text{X}}_2{\text{Y}}_3$.

Answer: ${\text{X}}_2{\text{Y}}_3$