Question

Metallic iron crystallizes in cubic lattice (pc, fee, or bee). The unit cell edge length is 287 pm. The density of iron is 7.87 g/cm . The molar mass of Fe is 55.85 g/mol. 1 cm = 101degree pm How many iron atoms are within a unit cell? What type of cubic unit cell?

Answer 1

In general, Iron is a BBC cubit unit cell, and the calculus of it's atoms will prove it:

length unit cell = 287 pm * 1 cm / 10¹⁰ pm = 2.87x10^-8 cm

Volume unit cell = (2.87x10^-8)³ = 2.36x10^-23 cm³

mass of Iron = 2.36x10^-23 * 7.87 = 1.86x10^-22 g

Atoms = 1.86x10^-22 * 6.02x10²³ atoms/mol = 112 g * atoms

If the molecular mass of IRon is 55.87 then:

number of atoms = 112 / 55.8 = 2.01 atoms

Hope this helps.