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9 November, 11:56

The coinage metals - - copper, silver, and gold - - crystallize in a cubic closest packed structure. Use the density of silver (10.5 g/cm3) and its molar mass (107.9 g/mol) to calculate an approximate atomic radius for silver.

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  1. 9 November, 12:15
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    The answer to the question is

    The approximate atomic radius for silver is 1.445*10⁻⁸ cm

    Explanation:

    To solve the question we list out the known variables as follows

    The density of silver = 10.5 g/cm³

    Molar mass of silver = 107.9 g/mol

    Number of moles in one cm³ of silver = 10.5/107.9 moles or 0.0973 moles

    Avogadro's law states that equal volumes of all substances contain equal number of particles that is one mole of any substance contain 6.022 * 10²³ elementary particles

    Therefore one mole of silver contains 6.022 * 10²³ silver atoms

    number of moles of silver in a unit cell = 4/6.022 * 10²³ or 6.642 * 10⁻²⁴ mol which has a mass = 6.642 * 10⁻²⁴ mol * molar mass of silver or 7.167 * 10⁻²² g

    Therefore the volume of a unit cell is given by Volume = mass/density =

    7.167 * 10⁻²² g/10.5 g/cm³ = 6.83 * 10⁻²³ cm³

    The diagonal of the face of a unit cell contains four atomic silver radius therefore

    That is 4 * silver radius = diagonal of cubic unit cell face

    = √2 * ∛ (6.83 * 10⁻²³ cm³)

    The approximate atomic radius for silver = (1/4) * √2 * ∛ (6.83 * 10⁻²³ cm³)

    = 1.445*10⁻⁸ cm
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