When platinum crystallizes, it forms face-centered cubic cells. The unit cell edge length is 392.3 pm. Calculate the density of platinum in g/cm3.?

1 cm = (10 * 10^10) pm

Therefore;

the unit length of the cell is equivalent to 3.923 * 10^-8 cm

The volume of the cubic cell is given by (length) ³

= (3.923*10^-8) ³

= 6.0375 * 10^-23 cm³

Density is calculated by dividing mass with the volume

The atomic mass of platinum 195.064 g/mol,

Therefore,

The average mass of one atom is; (Avogadro's constant = 6.0*10^23 particles)

195.064 : 6.022 * 10^23 atoms/mol

= 3.239 * 10^-22 g/atom

The mass of the 4 platinum atoms in the face centered cubic unit cell:

(3.239 * 10^-22) * 4 = 129.56 * 10^-23 g/unit cell

Therefore;

Density = (129.56 * 10^-23) : (6.0375 * 10^-23)

= 21.459 g/cm³