Atoms of element B form hcp lattice and those of the element A occupy \(\frac{2^{rd}}{3}\) of octahedral voids. What is the formula of the compound formed by the element A and B?

\(A_4B_3\)

The correct answer is option 2. \(A_4B_3\).

Note: The given answer is as per the NTA answer key. However, there appears to be an issue in the framing of the question by NTA. For Option (2) to be correct, the question should refer to tetrahedral voids instead of octahedral voids. Since the question states octahedral voids, the chemically correct formula should be  $A_2B_3$ which is not available among the options. This is explained below:

Let the number of atoms of element B (forming the hcp lattice) be n.

In an hcp lattice: Number of octahedral voids = n

Element A occupies 2/3 of these available octahedral voids.

Number of atoms of element A = $\frac{2}{3} \times n = \frac{2n}{3}$

Ratio $A : B = \frac{2n}{3} : n$ = 2 : 3

The ratio of atoms is $A_2B_3$. Therefore, the chemically correct formula of the compound is $A_2B_3$.