A compound is formed by two elements \(P\) and \(Q\). Atoms of the element \(Q\). Atoms of the element \(Q\) (Anions) make hcp lattice and those of the element \(P\) (cations) occupy \(\frac{1}{8}\)th of the tetrahedral voids. What us the formula of the compound?

\(PQ_4\)

The correct answer is option 1. \(PQ_4\). 

Given:

Atoms of element \(Q\) (anions) form a hexagonal close-packed (hcp) lattice.

Atoms of element \(P\) (cations) occupy \(\frac{1}{8}\)th of the tetrahedral voids.

In an hcp lattice, the number of tetrahedral voids is twice the number of atoms of element \(Q\) (which form the lattice).

Therefore, if there are \(N\) atoms of \(Q\), there are \(2N\) tetrahedral voids.

Since the cations \(P\) occupy \(\frac{1}{8}\)th of the tetrahedral voids, the number of \(P\) atoms is:

\(\text{Number of } P \text{ atoms} = \frac{1}{8} \times 2N = \frac{N}{4}\)

The ratio of the number of \(P\) atoms to \(Q\) atoms is \(\frac{N/4}{N} = \frac{1}{4}\).

Thus, for every \(1\) atom of \(P\), there are \(4\) atoms of \(Q\).

This gives the formula of the compound as \(PQ_4\).

Thus, the correct answer is option 1. \(PQ_4\)