Question

Iron has a density of 7.8740g/cm3, and a radius of 126pm/iron atom. In what type of crystal lattice is it arranged?

Answer 1

Given that:

Density of iron, D = 7.8750 g/cm³

Molar mass of iron, M = 56 g/mol

Avogadro number, N_A = 6.022 x 10²³

For a unit cell, Density is given by:

Where Z represents no.of atoms in unit cell and a is the side length of the unit cell.

Substituting the given values:

Now we need to do trial and error method, substitute different values for different unit cells and check whether the LHS and RHS are matching.

For Face centered cubic cell (FCC):

Z = 4 atoms

That is Z/a³ matches with z/a³ value that we found from density.

Hence the unit cell of iron will be Face centered cubic cell (FCC).