View source for Born–Mayer equation

The '''Born–Mayer equation''' is an equation that is used to calculate the [[lattice energy]] of a crystalline [[ionic compound]]. It is a refinement of the [[Born–Landé equation]] by using an improved repulsion term.<ref>{{cite web|url=http://alpha.chem.umb.edu/chemistry/ch370/CH370_Lectures/Lecture%20Documents/Ch07_2_LatticeEnergy.pdf|title=Lattice Energy}}</ref>

:<math>E =- \frac{N_AMz^+z^- e^2 }{4 \pi \epsilon_0 r_0}\left(1-\frac{\rho}{r_0}\right)</math>
where:
*''N''<sub>A</sub> =  [[Avogadro constant]];
*''M'' = [[Madelung constant]], relating to the geometry of the crystal;
*''z''<sup>+</sup> = charge number of cation
*''z''<sup>−</sup> = charge number of anion
*''e'' = [[elementary charge]], 1.6022{{e|&minus;19}} [[coulomb|C]]
*''&epsilon;''<sub>0</sub> = [[permittivity of free space]]
*:4{{pi}}''&epsilon;''<sub>0</sub> = 1.112{{e|&minus;10}} C<sup>2</sup>/(J·m)
*''r''<sub>0</sub> = distance to closest ion
*''ρ'' = a constant dependent on the compressibility of the crystal; 30 [[picometer|pm]] works well for all alkali metal halides

==See also==
*[[Born–Landé equation]]
*[[Kapustinskii equation]]

==References==
{{reflist}}

{{DEFAULTSORT:Born-Mayer Equation}}
[[Category:Solid-state chemistry]]
[[Category:Ions]]