Consider a cubic crystal of lattice constant ‘a’.

The density of the crystal = ρ

Volume of the unit cell = a³

Eqn 1

Mass in each unit cell = ρa³

[latex] \left(\because \text { Density }=\frac{\text { Mass }}{\text { Volume }}\right) [/latex]

The number of atoms per unit cell = n

The atomic weight of the material = M

Avogadros number = N

(number of molecules per kg mole of the substance)

Mass of each molecule [latex] =\frac{M}{N} [/latex]

where, M is atomic weight

Eqn 2

Mass in each unit cell [latex] =\mathrm{n} \times \frac{\mathrm{M}}{\mathrm{N}} [/latex]

(for n atoms)

From equations (1) and (2), we have

[latex] \rho a^3=\frac{n M}{N} \quad \text { or } \quad \rho=\frac{n M}{N a^3} [/latex]

[latex] \rho=\frac{(\text { Number of atoms per unit cell }) \times(\text { Atomic weight })}{(\text { Avogadros number }) \times(\text { Lattice cons } \tan t)^3} [/latex]

From the above equation, the value of lattice constant ‘a’ can be calculated.