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GATE 2023 CY – Question 24

Inorganic Chemistry · Solids: Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structure of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors, Zeolites and their applications. · 1 mark · Multiple choice

The packing efficiency (in %) of spheres for a body-centered cubic (bcc) lattice is approximately

  1. 74
  2. 68
  3. 60
  4. 52

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Correct answer: (B) 68

Explanation

The body diagonal gives 4r=√3a, and there are two spheres per cell. Packing fraction=2(4πr³/3)/a³=π√3/8=0.68017.

Thus the efficiency is about **68%, B**. The74% value applies to close-packed fcc/hcp arrangements.