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17 December, 01:33

The radius of a single atom of a generic element x is 197 picometers (pm and a crystal of x has a unit cell that is face-centered cubic. calculate the volume of the unit cell.

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  1. 17 December, 03:40
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    In a face centered cubic unit cell, the volume occupied by the particles of the substance is about 74% of the total unit cell. First, we find the volume of a single atom assuming it to be sphere:

    Volume (atom) = 4/3 x π x r³

    Volume (atom) = 4/3 x π x (197 x 10⁻¹²) ³

    Volume (atom) = 2.87 x 10⁻²⁹ m³

    There are a total of 4 atoms in a FCC unit cell, so the total volume occupied by atoms is:

    2.87 x 10⁻²⁹ x 4

    = 1.15 x 10⁻²⁸ m³

    Volume of cell = (1.15 x 10⁻²⁸) / 0.74

    Volume of cell = 1.55 x 10⁻²⁸ m³
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