Q.72 Chemistry ⭐ 360° Option Elimination Active

NEET 2023 Chemistry Question 72 Solution

Topic: Solid State · Official NTA Booklet Code G5

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

✓

Verified Against NTA Final Answer Key

Option (2) : 5

📚 Solid State Easy

📋 Given Parameters & Problem Setup

Element B lattice Cubic close packed (ccp / fcc)

Element A occupancy 1/3 of tetrahedral voids

Formula of compound A_x B_y

Target quantity x + y

⚡

The 30-Second Exam Hall Shortcut: ⚡ Void Ratio Rule: N atoms in ccp ⟹ 2N Tetrahedral Voids

⏱️ Save ~30 seconds

Let B = 1. Tetrahedral voids = 2. A occupies 1/3 of them ⟹ A = 2 × (1/3) = 2/3. Formula = A_(2/3) B_1 = A₂B₃ ⟹ x = 2, y = 3 ⟹ x + y = 2 + 3 = 5 in 10 seconds!

1 In any close-packed lattice (ccp or hcp), if there are N lattice atoms, the number of tetrahedral voids is exactly 2N.

2 Element B forms the ccp lattice ⟹ Number of B atoms = N.

3 Total number of tetrahedral voids = 2N.

4 Atoms of element A occupy 1/3 of these tetrahedral voids:

5 Number of A atoms = (1/3) × 2N = (2/3) N.

6 Ratio of atoms A : B = (2/3) N : N = 2/3 : 1 = 2 : 3.

7 Formula of compound is A₂B₃ (so x = 2 and y = 3).

8 Question asks for x + y: x + y = 2 + 3 = 5.

9 Lock Option (2) 5 immediately!

🛡️

Why You Can 100% Trust This Shortcut: Solid State · Close-Packed Structures (For N close-packed spheres, there are N octahedral voids and 2N tetrahedral voids).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Number of Voids in a Cubic Close-Packed (ccp) Array

In a cubic close packed (ccp / face-centered cubic) lattice of spheres, let the number of close-packed constituent atoms forming the lattice be N. Geometrical packing dictates that the number of octahedral voids is N, and the number of tetrahedral voids is 2N:

\text{Number of B atoms} = N, \qquad \text{Total tetrahedral voids} = 2N

Step 2

Calculation of Constituent Atoms of Element A

Atoms of element A occupy one-third (1/3) of the available tetrahedral voids. Therefore, the total number of atoms of A per N atoms of B is:

\text{Number of A atoms} = \frac{1}{3} \times 2N = \frac{2}{3} N

Step 3

Determination of the Simplest Empirical Formula

Find the simplest whole-number stoichiometric ratio between elements A and B:

A : B = \frac{2}{3} N : N = \frac{2}{3} : 1 = 2 : 3 \implies \text{Formula} = A_2 B_3

Step 4

Evaluation of the Requested Sum (x + y)

Comparing the empirical formula A₂B₃ with A_x B_y identifies x = 2 and y = 3. Computing their sum:

x = 2, \quad y = 3 \implies x + y = 2 + 3 = 5

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Represents only subscript x, not the sum x + y.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate gave only the value of x.

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate sum of subscripts: In A₂B₃, x = 2 and y = 3 ⟹ x + y = 5.

💡

Why this is airtight: None. Candidate correctly determined formula and calculated the sum.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Result of assuming tetrahedral voids equal N instead of 2N (A_(1/3) B_1 = AB₃ ⟹ 1 + 3 = 4).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate forgot the factor of 2 for tetrahedral voids (confused with octahedral voids).

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Represents only subscript y, not the sum x + y.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate gave only the value of y.

⚠️

NTA Trap Alert: Confusing Tetrahedral Voids (2N) with Octahedral Voids (N)

If a student mistakenly assumes there are N tetrahedral voids per N lattice atoms, they calculate A = (1/3)N ⟹ AB₃ ⟹ x + y = 1 + 3 = 4 (Option 3). In close-packed lattices, tetrahedral voids are ALWAYS TWICE the number of lattice spheres (2N)!

🛡️ How to avoid the -1 mark: Void Rule: Tetrahedral = 2N, Octahedral = N.

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Solid State Standard Benchmark

Core Scientific Principle Tested:

"Number of tetrahedral voids generated is double the number of close-packed particles. A occupies 1/3 of 2N ⟹ A₂B₃ ⟹ x + y = 5."

Syllabus Focus: Formula of a Compound and Number of Voids Filled

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Chemistry Question 72 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Void Ratio Rule: N atoms in ccp ⟹ 2N Tetrahedral Voids

Step-by-Step Rigorous Workflow & Mathematical Proof

Number of Voids in a Cubic Close-Packed (ccp) Array

Calculation of Constituent Atoms of Element A

Determination of the Simplest Empirical Formula

Evaluation of the Requested Sum (x + y)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Tetrahedral Voids (2N) with Octahedral Voids (N)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — The Solid State

Hexagonal Primitive Unit Cell: Number of Atoms, Tetrahedral and Octahedral Voids

14 Bravais Lattices: Count of Body-Centred Unit Cells

Body Centered Cubic (BCC) Lattice: Relationship Between Edge Length and Atomic Radius

Octahedral Voids in Face-Centred Cubic (fcc) Unit Cell

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