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
