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The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 [ 1 ] 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.
n is the Born exponent (a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically). [6] The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors:
The Born equation can be used for estimating the electrostatic component of Gibbs free energy of solvation of an ion. It is an electrostatic model that treats the solvent as a continuous dielectric medium (it is thus one member of a class of methods known as continuum solvation methods). It was derived by Max Born. [1] [2]
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
The Madelung constant allows for the calculation of the electric potential V i of the ion at position r i due to all other ions of the lattice = where = | | is the distance between the i th and the j th ion.
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.
Exponentiation with negative exponents is defined by the following identity, which holds for any integer n and nonzero b: =. [1] Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (). [24]
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that ...