Born–Landé equation

The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.

${\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \varepsilon _{0}r_{0}}}\left(1-{\frac {1}{n}}\right)}$

where:

• N_A = Avogadro constant;
• M = Madelung constant, relating to the geometry of the crystal;
• z⁺ = numeric charge number of cation
• z⁻ = numeric charge number of anion
• e = elementary charge, 1.6022×10⁻¹⁹ C
• ε₀ = permittivity of free space

  4πε₀ = 1.112×10⁻¹⁰ C²/(J·m)

• r₀ = distance between closest cation [ +ve ] & anion [ -ve ].
• n = Born exponent, typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
• E = Lattice energy is expressed by 'E' .