A compound contains elements X and Y. Y atoms form CCP lattice and atoms of X occupy 1/3rd of tetrahedral voids. What is the molecular formula of the compound ?

Let a unit cell be divided into eight small cubes in which each small cube has atoms at alternate corners. It means there are 4 atoms in each small cube, which form a regular tetrahedron when joined together. In this tetrahedron there is a tetrahedral void. In whole there are 8 tetrahedral voids in all 8 tetrahedrons. Hence, we conclude that the number of tetrahedral voids is double the number of lattice points.

So now,
No. of tetrahedral voids in CCP = 2× no. of atoms of Y
Atoms of Y in CCP unit cell is always = 4
So tetrahedral void = 2× 4 = 8

Number of tetrahedral voids occupied by element x$=\frac{1}{3}\times 8$
Now ratio of element X with that of y =$\frac{8}{3}+\frac{1}{4}$
The ratio comes to be $$2:3$$
Hence the formula will be X₂Y₃.