Chemistry - Solid State Question with Solution | TestHub

Element Y forms a face-centered cubic (FCC) lattice.

Number of Y atoms per unit cell = $4$

Number of tetrahedral voids in an FCC unit cell = $2\times 4=8$

Element X occupies one-third of the tetrahedral voids.

Number of X atoms per unit cell = $\frac{1}{3}\times 8=\frac{8}{3}$

Ratio of X to Y = $\frac{8}{3}:4=8:12=2:3$

The formula of the compound is $X_2{Y}_3$.