Question

how to find density when given the radius of a body-centered cubic cell

Answer 1

Calculation of density of unit cell

Knowing the unit cell dimensions, the density of a crystalline substance can be calculated as follows:

Let the molecular weight of a crystalline substance be ‘M’. Let the Avogadro’s number be ‘N₀’. ‘Z’ is the number of atoms present per unit cell and ‘p’ is the density of the unit cell or of the substance. The unit cell length is ‘a’, so that the volume of the unit cell is ‘a³’ (=V). Then the mass corresponding to each lattice point = .

The mass of ‘Z’ lattice points = .

i.e. density of the unit cell = = =

ρ =

Where

ρ = density

Z = no. of atoms per unit cell = for BCC = 2

M = mol. Wt. of the lattice particle

a = unit cell length.