UNIT 1- SOLID STATE (Packing Efficiency) XII CHEMISTRY PART IV CBSE

 

1. Packing Efficiency

• Packing efficiency is the percentage of total space occupied by particles (atoms, ions, or molecules) in a crystal lattice.
• Packing Efficiency=Volume occupied by atoms/Total volume of the unit cell x100

A. Simple Cubic (SC)

• Atoms per unit cell: 1

• Coordination number: 6

• Edge length: $\mathrm{<span\; style="font-size:\; medium;">a</span>}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">2</span>}\mathrm{<span\; style="font-size:\; medium;">r</span>}$

• 1×4/3​πr3​/a3×100=π​/6×100=52.4%

• Empty space (voids): 47.6%

B. Body-Centred Cubic (BCC)

• Atoms per unit cell: 2

• Coordination number: 8

• Relation: $\sqrt{3}a = 4r$
  

• Packing Efficiency:

• 2×4​/3πr3​/a3×100=68%

• Empty space: 32%

C. Face-Centred Cubic (FCC) / Cubic Close Packed (CCP)

• Atoms per unit cell: 4

• Coordination number: 12

• Relation: $\sqrt{2}a = 4r$
  

• Packing Efficiency:

• 4×4/3​πr3​/a3×100=74%

• Empty space: 26%

D. Hexagonal Close Packed (HCP)

• Atoms per unit cell: 6 (effective)

• Coordination number: 12

• Packing Efficiency: 74% (same as FCC)

• Arrangement: ABABAB… layers