Atoms of element B form hcp lattice and those of the element A occupy 2/3 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?

Concept : 

• Hexagonal close packing (HCP) is a type of crystal structure where atoms or ions are arranged in a close-packed pattern in three dimensions.
• In this arrangement, each atom has 12 nearest neighbors, with six arranged in a regular hexagonal pattern around it, and the other six forming an equilateral triangle above and below it.
• The HCP structure is one of the most efficient ways to pack spheres together, and it is found in many metallic and non-metallic elements

Explanation : 

In Hexagonal close packing (HCP) structure if the number of close packed spheres are N then the number of octahedral voids generated is N and the number of tetrahedral voids generated is 2N

Now, According to question, Atoms of element B form hcp lattice that means the number of atoms of element B will be 6 and thus, there will be 12 tetrahedral voids.

And as A occupy  of tetrahedral void.

Thus, Number of A =  × 12

Number of A= 8

Hence, the formula of the compound formed by the elements A and B is A₈B₆ which can be simplified to A4B3

Conclusion:

Therefore, the formula of the compound formed by the elements A and B is A4B3