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

The hcp lattice is formed by element `B`
First method
`:. Z_(eff)` of `B` (hcp lattice) `= 6`
Number of `TV = 8//"unit cell"`
Number of `OV = 4//"unit cell"`
Since elements `A` occupies two-thirds of `TV_(s)`
`:.` Number of `A = (2)/(3) xx 12 = 8`
`:.` Formula `= A_(8)B_(6) = A_(4)B_(3)`
Second method
Let `Z_(eff)` of `B = 1`
Number of `TV = 2//"atom"`
Number of `OV = 1//"atom"`
`:.` Number of `A = (2)/(3) xx TV = (2)/(3) xx 2 = (4)/(3)`
`:.` Formula `= A_(4//3)B_(1)`
Simplifying: `A_(4)B_(3)`