In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is . The value of is ______. [nearest integer]
Answer: 3
Solution
In ccp (fcc) arrangement:
When two A atoms from opposite faces are removed:
A atoms remaining = 4 - 2 × (1/2) = 4 - 1 = 3
B atoms remain = 4
Resultant stoichiometry: A₃B₄
Therefore, x = 3
- A atoms: 8 corners × 1/8 + 6 faces × 1/2 = 1 + 3 = 4 atoms per unit cell
- B atoms in octahedral sites: 12 edges × 1/4 + 1 center = 3 + 1 = 4 atoms per unit cell
When two A atoms from opposite faces are removed:
A atoms remaining = 4 - 2 × (1/2) = 4 - 1 = 3
B atoms remain = 4
Resultant stoichiometry: A₃B₄
Therefore, x = 3
JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Integer answer