Atoms of elements `B` from hcp 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

Suppose number of atoms B in hcp lattic = n
As number of tetrahedral voids is double the number of atoms in the close packing . Therefore, number of tetrachedral voids = 2n.
As atoms A occupy 2/3rd of the tetrahedral voids, therefore, number of atoms A in the lattic `= 2/3 xx 2n = ( 4n) /3`
Ratio of A : B = `(4n)/2 : n = 4/3 : 1= 4:3 `
Hence, the formula of the compound ` A_(4)B_(3) `