where the proportionality constant K depends on the polarizability of the molecules constituting the dielectric.
For a molecular dielectric consisting of a single kind of non-polar molecules, the proportionality factor K (m3/kg) is,
Here NA is Avogadro's constant, α is the molecular polarizability of one molecule, and ε0 is the electric constant (permittivity of the vacuum). In this expression for PM it is assumed that the molecular polarizabilities are additive; if this is not the case, the expression can still be used when α is replaced by an effective polarizability. The factor 1/3 arises from the assumption that a single molecule inside the dielectric feels a spherical field from the surrounding medium. Note that α / ε0 has dimension volume, so that K indeed has dimension volume per mass.
In Gaussian units (a non-rationalized centimeter-gram-second system):
and the factor 103 is absent from K (as is ε0, which is not defined in Gaussian units).
For polar molecules a temperature dependent contribution due to the alignment of dipoles must be added to K.
The Lorentz-Lorenz law follows from the Clausius-Mossotti relation by using that the index of refraction n is approximately (for non-conducting materials and long wavelengths) equal to the square root of the static relative permittivity (formerly known as static relative dielectric constant) εr,
- H. A. Lorentz, Über die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte [On the relation between the propagation speed of light and density of a body], Ann. Phys. vol. 9, pp. 641-665 (1880). Online
- L. Lorenz, Über die Refractionsconstante [About the constant of refraction], Ann. Phys. vol. 11, pp. 70-103 (1880). Online