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Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e , or exactly 1 e , −1 e , 2 e , etc., but not 1 / 2 e , or −3.8 e , etc.
Charge number (denoted z) is a quantized and dimensionless quantity derived from electric charge, with the quantum of electric charge being the elementary charge (e, constant). The charge number equals the electric charge ( q , in coulombs ) divided by the elementary charge: z = q / e .
z + and z − are the numbers of elementary charge on the cation and anion, respectively, and r + and r − are the radii of the cation and anion, respectively, in meters. The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%.
The electrostatic potential energy, E pair, between a pair of ions of equal and opposite charge is: = where z = magnitude of charge on one ion e = elementary charge, 1.6022 × 10 −19 C ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m)
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The charge of an isolated system should be a multiple of the elementary charge e, even if at large scales charge seems to behave as a continuous quantity. In some contexts it is meaningful to speak of fractions of an elementary charge; for example, in the fractional quantum Hall effect. The unit faraday is sometimes used in electrochemistry.
z + = charge number of cation; z − = charge number of anion; e = elementary charge, 1.6022 × 10 −19 C; ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m) r 0 = distance to closest ion; ρ = a constant dependent on the compressibility of the crystal; 30 pm works well for all alkali metal halides