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🧪 Chemistry  ·  Solid State  ·  NEET & JEE

Calculate the fraction of total volume occupied in a simple cubic packing (SC) if radius r and edge length a = 2r:

Answer: π/6.

  • A π/4
  • B π/6
  • C π/3
  • D 2π/3

Correct answer: B. π/6

Explanation: Volume of one atom = (4/3)πr³. Volume of unit cell = a³ = (2r)³ = 8r³. Packing fraction = (4/3)πr³ / 8r³ = π/6 ≈ 0.5236 (52.36%).

Cubic Unit Cells: Atom PositionsSimple CubicCN=6, 52.4% packedBody-Centred (BCC)CN=8, 68% packedFace-Centred (FCC)CN=12, 74% packed (densest)Corner atoms (shared by 8 cells) shown lighter; body/face-centre atoms shown solid

The three cubic unit cells: Simple Cubic has atoms only at corners; Body-Centred adds one atom at the centre; Face-Centred adds one atom at the centre of each of the 6 faces, giving the highest packing efficiency.

Concept context

Explore the ordered world of crystalline solids: unit cells, packing, defects, and how structure determines electrical and magnetic properties.

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