Answer :

In ccp structure, each unit cell contains atoms at all the corners and at the centre of all the faces of the cube. Each atom at a corner is shared between eight adjacent unit cells, four unit cells in the same layer and four unit cells of the upper (or lower) layer. Only 1/8th of a particle actually belongs to a particular unit cell. The atom at the faces is also shared with the adjacent unit cell, both sharing half of the atom i.e. only 1/2 of each atom belongs in the unit cell.

To calculate number of atoms per unit cell of ccp,

8 corner atoms * 1/8 atom per unit cell = 8 x 1/8 = 1 atom

6 face-centered atoms * 1/2 atom per unit cell = 6 x 1/2 = 3 atoms

Total atoms in unit cell = 1 + 3 = 4 atoms.

The number of tetrahedral voids is twice the number of atoms and octahedral voids is same as the number of atoms.

In cubic closed packed (ccp) lattice, number of atoms per unit cell = 4.

Number of tetrahedral voids present = 2 x number of atoms per unit cell = 2 x 4 = 8.

Given that atoms of X occupy 2/3rd of tetrahedral voids, M = 2/3 x 8 = 16/3

So the ratio of X and Y in a unit cell is X:Y = 16/3:4 = 4/3:1

The formula of the compound is X4Y3.

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