A solid is made up of two elements \(X\) and \(Y\). \(X\) occupies \(2/3\)rd of the octahedral voids and \(Y\) has ccp arrangement. What is the formula of the compound \(X\) and \(Y\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → X2Y3
In a close-packed (ccp) arrangement the number of octahedral voids equals the number of close-packed particles.
Let the number of Y atoms (ccp) = N
Number of octahedral voids = N
X occupies 2/3 of them, so number of X atoms = 2N/3
X : Y = 2N/3 : N = 2 : 3
The formula is X2Y3 (the same pattern as \( \ce{Al2O3} \), where \( \ce{Al^{3+}} \) fills two-thirds of the octahedral voids).
Why the other options are incorrect
Option (1) XY — Incorrect. Would need X in all the octahedral voids (1 : 1), as in NaCl.
Option (3) X3Y2 — Incorrect. Reverses the ratio; it would need more X atoms than there are octahedral voids.
Option (4) X2Y — Incorrect. Would need X in all the tetrahedral voids (2N of them), not two-thirds of the octahedral voids.
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
