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