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?

<p>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.</p> <p>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.</p> <p>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.</p> <p>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 $2 : 3$.</p> <p>So, the formula of the compound is $\mathrm{X_2Y_{3}}$</p>