Atoms of elements `B` from hep lattice and those of element `A` occupy two-thirds of tetrahedral voids. What is the formula of the compound formed by elements `A` and `B`?

Explanation

Let the number of atoms of B in hcp lattice = n
Since the numberof tetrahedral voids is double the number of atoms in close packed arrangement.
`therefore" "`Number of tetrahedral voids = 2n.
Since only 2/3 of tetrahedral voids are occupied by the atoms of the element A.
`therefore" Number of atoms of A in hcp lattice"=2nxx2//3=4n//3`.
Ratio of `A:B=4n//3:n=4n:3n=4:3`
The formula of compound AB = `A_(4)B_(3)`.