A solid has a cubic structure in which X atoms are located at the corners of the cube, Y atoms are at the cube centres, and O atoms are at the edge centers. What is the formula of the compound is XYO_a?. The value of a is

 

Atoms of X are present at all eight corners of the cube. Therefore, each atom of X at the corner makes 1/8 contribution toward the unit cell.

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

Y atom is present at the body center, thus contribution of Y toward unit cell- 1× 1= I
O atom is present at each of the edge center (number of edges of cube = 12)
And each O atom present at edge center will make 1/4 contribution toward the unit cell.

$\text{ The number of }\mathrm{O}\text{ atoms per unit cell }=12\times \frac{1}{4}=3$

The formula of the compound is, therefore, XYO₃