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A metallic element crystallizes into a lattice containing a sequence of hexagonal layers of ABABAB....... What percentage by volume of this lattice is empty space?

Options

  1. A26%
  2. B74%
  3. C50%
  4. D85%

Correct answer

A. 26%

Step-by-step solution

Number of atoms in hcp is 6 per unit cell. Packing fraction = 6 × 4 3 πr 3 Base area × C Base area = 6 × 3 4 4 r 2 C = 4r 2 3 Packing fraction = π 3 2 = 0 . 74 Void % = 1 - 0 . 74 × 100 = 26 %

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