A metallic element crystallises into a lattice containing a sequence of layers ABABAB.... Any packing of spheres leaves out voids in the lattice. Percentage of empty space (by volume) is 52% 48% 50% 74%

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Arun · Answer

Dear student For a hcp unit cell, there are 6 atoms per unit cell. If r is the radius of the metal atoms, volume occupied by the metallic Atoms 6 * 4/3 * π * r 3 = 6 * 1.33 * 22/7 * r 3 = 25.08 * r 3 Geometrically it has been shown that the base area of hcp unit cell = 6 * √3/4 * 4r 2 and the height = 4r * √2/3 ∴ Volume of the unit cell = Area * height = 6 * √3/4 * 4r 2 * 4r * = 33.94 r 3 ∴ Volume of the empty space of one unit cell = 33.94 r 3 – 25.08 r 3 = 8.86 r 3 ∴ Percentage void = 8.816 r 3 /33.94 r 3 * 100 = 26.1% Regards Arun

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A metallic element crystallises into a lattice containing a sequence of layers ABABAB.... Any packing of spheres leaves out voids in the lattice. Percentage of empty space (by volume) is 52% 48% 50% 74%

A metallic element crystallises into a lattice containing a sequence of layers ABABAB.... Any packing of spheres leaves out voids in the lattice. Percentage of empty space (by volume) is

52%

48%

50%

74%

1 Answers

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