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12 June, 03:14

Rhodium has a face-centered cubic structure and has a density of 12.4 g/cm3. What is its atomic radius? (Note: for a face-centered cubic structure,)

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  1. 12 June, 03:19
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    For face centered cubic structure, no of atoms in a cell will be 4.

    so n = 4

    density = n x atomic mass / a³ x N

    N is avogrado no

    12.4 = n x 103 / (a³ x 6.02 x 10²³)

    a³ = 4 x 103 / (12.4 x 6.02 x 10²³)

    = 5.52 x 10⁻²³

    = 55.2 x 10⁻²⁴

    a = 3.8 x 10⁻⁸ cm

    if atomic radius is r

    a = 2√2 x r

    r = a / 2√2

    = 3.8 x 10⁻⁸ / 2√2 cm

    = 1.34 x 10⁻⁸ cm
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