The Rydberg–Ritz combination principle is an empirical rule proposed by Walther Ritz in 1908 to describe the relationship of the spectral lines for all atoms, as a generalization of an earlier rule by Johannes Rydberg for the hydrogen atom and the alkali metals.
The principle states that the spectral lines of any element include frequencies that are either the sum or the difference of the frequencies of two other lines.
Another related version is that the wavenumber or reciprocal wavelength of each spectral line can be written as the difference of two terms.
[3][4] The simplest example is the hydrogen atom, described by the Rydberg formula where
[3] The exact Ritz Combination formula was mathematically derived from this where: Where:
[7][8] The combination principle is explained using quantum theory.
Light consists of photons whose energy E is proportional to the frequency ν and wavenumber of the light: E = hν = hc/λ (where h is the Planck constant, c is the speed of light, and λ is the wavelength).
According to the quantum theory of the hydrogen atom proposed by Niels Bohr in 1913, an atom can have only certain energy levels.
On dividing by hc, the photon wavenumber equals the difference between two terms, each equal to an energy divided by hc or an energy in wavenumber units (cm−1).
Energy levels of atoms and molecules are today described by term symbols which indicate their quantum numbers.
Also, a transition from an initial to a final energy level involves the same energy change whether it occurs in a single step or in two steps via an intermediate state.
[9] The spectral lines of hydrogen had been analyzed and found to have a mathematical relationship in the Balmer series.
In 1908 Ritz derived a relationship that could be applied to all atoms which he calculated prior to the first 1913 quantum atom and his ideas are based on classical mechanics.