Question

If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.

Answer 1

Before any calculations, we need to determine first the crystal structure of the lead metal. From literature, the lead metal assumes an FCC structure. So, it would have 4 atoms per units cell where the three atoms is the sum of all the portion of an atoms in each face of the cell and the 1 atom is the sum of all the portion of the corner atoms. The volume of the unit cell is equal to the edge length raise to the power three or V = a^3. The edge length can be calculated from the radius of the atoms by the pythagorean theorem. We do as follows:

V = a^3
   a^2 + a^2 = (4r)^2
  2a^2 = (4r)^2
    a = 2r
V = (2r)^3
V = 16r^3
V = 16 (0.175x10^-9)^3
V = 1.21 x 10^-28 m^3