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?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(A_4B_3\)
When N particles are close packed (ccp/fcc or hcp), two kinds of voids are formed: the number of octahedral voids is N and the number of tetrahedral voids is 2N. The formula of a compound follows from how many of these voids the second kind of atom fills.
Let the number of atoms of B in the hcp lattice be N. Then:
\( \displaystyle \text{Tetrahedral voids} = 2N \)
Atoms of A occupy two third of them:
\( \displaystyle \text{Atoms of A} = \frac{2}{3} \times 2N = \frac{4N}{3} \)
\( \displaystyle \text{A : B} = \frac{4N}{3} : N = 4 : 3 \)
So the formula of the compound is A4B3.
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
