Question

Metallic iron crystallizes in a type of cubic unit cell. The unit cell edge length is 287 pm. The density of iron is 7.87 g/cm^3. How many iron atoms are there within one unit cell?

Answer 1

Given :

Length of unit cell = 287 pm = 287 x 10^-12 m

Density = 7.87 g / cm³

This is type of cubic cell so

Volume = ( 287 E-12 m)³ = 2.36 E-29 m^3

Calculation of mass in unit cell.

Mass = density x volume

Lets convert volume into cm^3 .

1 m^3 = 1000000 cm^3

Volume in cm^3 = 2.36 E-29 m^3 x 1000000 cm^3 / 1 m^3

= 2.36 E-23 cm^3

Mass in a unit cell = (7.87 g / cm^3 ) x 2.36 E-23 cm^3

= 1.86 E-22 g

Calculation of moles of iron

Mol of iron = 1.86 E-22 g / molar mass of Fe = 1.86 E-22 g / 55.845 g per mol = 3.33E-24 mol

Now 1 mol Fe = 6.02 E23 Fe atoms

Number of atoms in 3.33 E-24 = 3.33 E-24 1 mol Fe x 6.02 E23 Fe atoms/ 1 mol Fe= 2.0

= 2

So the number of Fe atoms in unit cell = 2