Question

In ionic crystalline solid atoms of element Y form hcp lattice. The atoms of element X occupy one-third of tetrahedral voids. What is the formula of the compound?

Answer 1

Given: Atoms of element Y form hcp structure.
Atoms of element X occupy 1/3rd of tetrahedral voids

To find: Formula of the compound

Calculation: The atoms of element Y form hcp structure.
The number of tetrahedral voids generated is twice the number of Y atoms.
Thus, number of tetrahedral voids = 2Y
The atoms of element X occupy (1/3) of these tetrahedral voids.
Hence, number of X atoms = 2Y × `1/3 = 2/3"Y"`

Ratio of X and Y atoms = `2/3`Y : 1Y = `2/3`: 1 = 2: 3

∴ Formula of compound = X₂Y₃