A compound is formed by two elements A and B. The element B forms cubic close packed structure and a

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Question

A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy 1/3 of tetrahedral voids. If the formula of the compound is AₓBᵧ, then the value of x + y is in option

Accepted Answer

Correct Answer: A — 5 (formula is A₂B₃)Step-by-step Solution:Step 1: In a cubic close packed (CCP/FCC) unit cell, the number of B atoms per unit cell = 4 (8 corner atoms × 1/8 + 6 face-centred atoms × 1/2 = 1 + 3 = 4).Step 2: Number of tetrahedral voids in CCP = 2 × number of atoms = 2 × 4 = 8 tetrahedral voids per unit cell.Step 3: A occupies 1/3 of tetrahedral voids → Number of A atoms = (1/3) × 8 = 8/3.Step 4: Ratio A : B = (8/3) : 4 = (8/3) : (12/3) = 8 : 12 = 2 : 3.Formula = A₂B₃ → x = 2, y = 3 → x + y = 5.Why other options are wrong:Option B (4): Would correspond to formula A₁B₃ or A₃B₁ — not obtained here.Option C (3): Would need x + y = 3 (e.g., AB₂ or A₂B) — not derived from 1/3 occupancy.Option D (2): Would require x = y = 1 (i.e., AB) — that would need ½ occupancy of tetrahedral voids.Key Concepts:In CCP (FCC) unit cell: Number of atoms = 4; Number of octahedral voids = 4; Number of tetrahedral voids = 8.In BCC: Number of atoms = 2; No octahedral/tetrahedral voids in the simple sense.Fraction × Total voids gives number of void-occupying atoms per unit cell.Formula is determined from the simplest whole number ratio of atoms per unit cell.

A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy 1/3 of tetrahedral voids. If the formula of the compound is AₓBᵧ, then the value of x + y is in option

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A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy 1/3 of tetrahedral voids. If the formula of the compound is AₓBᵧ, then the value of x + y is in option

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