A compound is formed by two elements \(P\) and \(Q\). 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 is the formula of the compound?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(PQ_4\)
In a close-packed (hcp or ccp) arrangement, the number of tetrahedral voids is twice the number of close-packed particles.
Let the number of Q atoms (forming hcp) = N
Number of tetrahedral voids = 2N
Number of P atoms = \( \displaystyle\frac{1}{8} \times 2N = \displaystyle\frac{N}{4} \)
P : Q = \( \displaystyle\frac{N}{4} : N \) = 1 : 4
So the formula is PQ4.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic is not there in the latest NCERT book (2026-27), and it is also out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Formula of a Compound and Number of Voids Filled – “Earlier in the section, we have learnt that when particles are close-packed resulting in either ccp or hcp structure, two types of voids are generated. While the number of octahedral voids present in a lattice is equal to the number of close packed particles, the number of tetrahedral voids generated is twice this number.”