Q.93 Chemistry ⭐ 360° Option Elimination Active
NEET 2023 Chemistry Question 93 Solution
Topic: The Solid State · Official NTA Booklet Code G5
Question
What fraction of one edge centred octahedral void lies in one unit cell of fcc?
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Verified Against NTA Final Answer Key
Option (4) : 1/4
📚 The Solid State Easy
📋 Given Parameters & Problem Setup
Lattice type Face-centred cubic (fcc)
Location of void Edge centre
Target fraction Fraction of one edge-centred octahedral void belonging to one unit cell
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⏱️ Save ~25 seconds The 30-Second Exam Hall Shortcut: ⚡ Lattice Sharing Geometry: 1 Cube Edge is Shared by Exactly 4 Unit Cells
In any cubic lattice, every edge is shared equally by 4 adjacent unit cells. Therefore, any atom or void located at an edge centre contributes exactly 1/4 of its volume to a single unit cell. Instant 5-second answer: 1/4 (Option 4)!
1 Visualize a cubic unit cell edge: four cubes meet along any single edge.
2 Contribution of any particle or interstitial void on an edge = 1/4.
3 Total edge-centred octahedral voids in fcc = 12 × (1/4) = 3.
4 Question specifically asks for the fraction of ONE edge-centred void: 1/4.
5 Select Option (4) directly.
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Why You Can 100% Trust This Shortcut: Fundamental 3D crystallographic geometry of cubic unit cells in NCERT.
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Step-by-Step Rigorous Workflow & Mathematical Proof
Step 1
Analyze Unit Cell Edge Sharing in Cubic Systems
In a three-dimensional cubic lattice, four unit cells share a common edge (two in the same horizontal layer and two in the layer directly above or below):
Step 2
Determine the Fraction of One Edge-Centred Void
Because an edge is divided equally among four unit cells, only 1/4 of any point, sphere, or void positioned at an edge centre belongs to any single unit cell:
Step 3
Differentiate Fraction from Total Count
A cube has 12 edges. The total contribution of all edge-centred octahedral voids to the unit cell is 12 × (1/4) = 3. Combined with 1 body-centred void (1 × 1 = 1), an fcc unit cell has 4 total octahedral voids, but the fraction of ONE edge void is strictly 1/4:
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4-Option Deep Scan
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
1 (1)
✗ Incorrect Verdict & Scientific Reason:
Confuses the total number of edges (12) with the geometric sharing fraction.
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Student Fallacy (Why candidates pick this trap): Candidate inverted the count of edges in a cube.
2 (2)
✗ Incorrect Verdict & Scientific Reason:
Fraction for a face-centred position (shared by 2 unit cells), not an edge-centred position.
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Student Fallacy (Why candidates pick this trap): Candidate confused edge-centred sharing with face-centred sharing.
3 (3)
✗ Incorrect Verdict & Scientific Reason:
Unphysical sharing factor in a cubic crystal system.
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Student Fallacy (Why candidates pick this trap): Candidate guessed an arbitrary fraction.
4 (4)
✓ 100% Correct Verdict & Scientific Reason:
Accurate: Each edge is shared among 4 unit cells, so contribution is exactly 1/4.
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Why this is airtight: None. Candidate correctly applied crystallographic sharing geometry.
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NTA Trap Alert: Confusing Total Contribution with Fraction of a Single Void
Some students compute the total contribution of all edge-centred voids: 12 × 1/4 = 3, and then look for 3. The question asks: "What fraction of ONE edge centred void lies in one unit cell?" The fraction of one void is simply 1/4.
🛡️ How to avoid the -1 mark: Read carefully: "fraction of one void" = 1/4, whereas "total number of edge voids per unit cell" = 3.
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Core NEET Syllabus Standard
National Eligibility cum Entrance Test (NEET UG) · The Solid State Standard Benchmark
Core Scientific Principle Tested:
"In a cubic unit cell, a position on an edge is shared equally by 4 unit cells, giving a contribution fraction of 1/4."
Syllabus Focus: Imperfections in Solids & Voids in fcc Lattice
Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗
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