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A metallic element crystallizes into a lattice containing a sequence layers of ABABAB ..... . Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space?

Correct answer

26

Step-by-step solution

Packing fraction in hcp = 6 × 4 3 π r 3 V o l u m e = 6 × 4 π r 3 3 × A r e a × H e i g h t Area (of base) of unit cell in hcp = 6 3 r 2 (follow text) height of unit cell in hcp = 4 r × 2 3 (follow text) So packing fraction = 6 × 4 π r 3 3 × 6 3 r 2 × 4 r × 2 3 = π 3 2 = 0.74 or = 74% Thus, empty space in hcp = 1 - 0.74 = 0.26 or = 26%.

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