Question

Lead (pb) has a density of 11.3 g/cm3 and crystallizes face-centered cubic. based on these data, calculate the radius (r) of the lead atom given that, for a face-centered unit cell: cube edge length = r√8.

Answer 1

Lead is said to have a face centered cubic crystal structure. So, it would have four atoms per cell where 3 of the atoms are at the faces and 1 atom constitutes the corner of the unit cell. So, that the diagonal of one face of the cell is equal to 4 times the radius. To determine the measurement of the radius, we calculate the volume from the density given.

Density = 11.3 g / cm^3 = 207.2 g / mol ( 4 atoms / cell ) / 6.022x10^23 atoms / mol (V cm^3/ cell)

Calculating for V,
V = 1.21795 x 10^-22 cm^3
V = a^3       where a is the edge length
a = ∛1.21795 x 10^-22 cm^3
a = 4.9569x10^-8 cm
diagonal = 4r
r = diagonal / 4

where diagonal = √2a^2 = a√2
r = a√2 / 4 = 1.7525x10^-8 cm