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.

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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