Question

Platinum crystallizes in a face-centered cubic cell. the density of platinum is 21.4 g/cm3. calculate the radius of the platinum atom in pm

Answer 1

1 mole of platinum has a mass of 195 g therefore 1 atom will have a mass of 195 g /(6.02 ×10^23) = 3.239 × 10^-22 g
Density is given by dividing mass by volume, thus to get volume, mass is divided by density. 
The volume = (3.239 × 10^-22)/21.4 
                    = 1.514 × 10^-23 cm³
But volume of a sphere is given by 4/3πr³
Therefore, r³ = 3.6129 × 10^-24 
                 r   = ∛(3.6129 × 10^-24)
                      = 1.534 × 10^ -8 cm
Therefore, the radius of the platinum atom is 1.534 × 10^-8 cm