A compound is formed from elements $\mathrm{X}$ and $\mathrm{Y}$. The atoms of $\mathrm{Y}$ (anions) form a $\mathrm{ccp}$ lattice. The atoms of $\mathrm{X}$ (cations) occupy half of the octahedral voids and half of tetrahedral voids. What is the formula of the compound?

The atoms $\mathrm{Y}$ form a $\mathrm{CCP}$ lattice means atoms are present at corners as well as the face centre.

So, the number of atoms of $\mathrm{Y}$ present in the unit cell $=4$

Number of tetrahedral voids present in $\mathrm{CCP}$$=8$

Number of octahedral void present in $\mathrm{CCP}=4$

So, the number of atoms of $\mathrm{X}$ present in the unit cell $=$ $\frac{1}{2}\times 8 +\frac{1}{2}\times 4 = 4+2 =6$

So, formula of unit cell : $$\begin{gathered} \mathrm{X} : \mathrm{Y} =6:4 \\ \mathrm{X} : \mathrm{Y} = 3:2 \\ \mathrm{i}.\mathrm{e}. {\mathrm{X}}_3{\mathrm{Y}}_2 \end{gathered}$$