Calculation Involving Unit Cell Dimensions

Calculation Involving Unit Cell Dimensions 

From the unit cell dimensions, it is possible to calculate the volume of the unit cell. Knowing the density of the metal. We can calculate the mass of the atoms in the unit cell. The determination of the mass of a single atom gives an accurate determination of Avogadro constant.

Suppose edge of unit cell of a cubic crystal determined by X – Ray diffraction is a, d is density of the solid substance and M is the molar mass, then in case of cubic crystal

Volume of a unit cell = a₃

Mass of the unit cell = no. of atoms in the unit cell × mass of each atom = Z × m

Here Z = no. of atoms present in one unit cell

m = mass of a single atom

Mass of an atom present in the unit cell = m/N_A

∴Density d = mass of unit cell/volume of unit cell = ZM/a³

d = Z.M/a³ x N_A

Note:

Density of the unit cell is same as the density of the substance

Other Resourceful Topics

• Imperfection in Solids
• Properties of Solids
• Super Conductivity