A compound is formed by two elements $\mathrm{X}$ and $\mathrm{Y}.$ The element $\mathrm{Y}$ forms cubic close packed arrangement and those of element $\mathrm{X}$ occupy one third of the tetrahedral voids. What is the formula of the compound?

Atoms of Element $\mathrm{Y}$, are present in cubic close packing. In cubic close packing the number of atoms per unit cell is $4$.

So, the effective number of element $\mathrm{Y}$, per unit cell is $4$

Element $\mathrm{X}$, are present at one third of the tetrahedral voids.

Number of tetrahedral void $=$Twice the number of atoms in unit cell

Number of atoms of Element $\mathrm{X}$ are present unit cell $=\frac{1}{3}\times 8=\frac{8}{3}$

$$\begin{gathered} \mathrm{X} : \mathrm{Y} \\ \frac{8}{3} : 4 \\ 2 : 3 \end{gathered}$$

Formula of the compound $={\mathrm{X}}_2{\mathrm{Y}}_3$