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

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