Rydberg–Ritz combination principle
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The Rydberg–Ritz combination principle is an empirical rule proposed by
Walther Ritz Walther Heinrich Wilhelm Ritz (22 February 1878 – 7 July 1909) was a Swiss theoretical physicist. He is most famous for his work with Johannes Rydberg on the Rydberg–Ritz combination principle. Ritz is also known for the variational method n ...
in 1908 to describe the relationship of the spectral lines for all atoms, as a generalization of an earlier rule by
Johannes Rydberg Johannes (Janne) Robert Rydberg (; 8 November 1854 – 28 December 1919) was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to describe the wavelengths of photons (of visible light and other electrom ...
for the hydrogen atom and the alkali metals. The principle states that the
spectral lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
of any element include frequencies that are either the sum or the difference of the frequencies of two other lines. Lines of the spectra of elements could be predicted from existing lines. Since the frequency of light is proportional to the
wavenumber In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to te ...
or reciprocal
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
, the principle can also be expressed in terms of wavenumbers which are the sum or difference of wavenumbers 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. The simplest example is the hydrogen atom, described by the
Rydberg formula In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...
:\frac = R\left(\frac-\frac\right) where \lambda is the wavelength, R is the
Rydberg constant In spectroscopy, the Rydberg constant, symbol R_\infty for heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first aro ...
, and n_1 and n_2 are positive integers such that n_1 < n_2. This is the difference of two terms of form T_n = \frac. The exact Ritz Combination formula was mathematically derived from this where: :\tilde \;=\; \frac, :\tilde = A- \frac Where: \tilde is the wavenumber, A is the limit of the series, N is a universal constant, (now known as R) m is the numeral, (now known as n) and are constants.


Relation to quantum theory

The combination principle is explained using quantum theory. Light consists of
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
s 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. A combination of frequencies or wavenumbers is then equivalent to a combination of energies. According to the quantum theory of the hydrogen atom proposed by
Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...
in 1913, an atom can have only certain
energy levels A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...
. Absorption or emission of a particle of light or
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
corresponds to a transition between two possible energy levels, and the photon energy equals the difference between their two energies. 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 symbol In quantum mechanics, the term symbol is an abbreviated description of the (total) angular momentum quantum numbers in a multi-electron atom (however, even a single electron can be described by a term symbol). Each energy level of an atom with a giv ...
s 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. The energy of transition in a single step is the ''sum'' of the energies of transition in two steps: (E3 – E1) = (E2 – E1) + (E3 – E2). The NIST database tables of lines of spectra contains observed lines and the lines calculated by use of the Ritz combination principle.


History

The spectral lines of
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
had been analyzed and found to have a mathematical relationship in the
Balmer series The Balmer series, or Balmer lines in atomic physics, is one of a set of six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empirical equation discovered b ...
. This was later extended to a general formula called the
Rydberg formula In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...
. This could only be applied to hydrogen-like atoms. 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.M A El'yashevich, N G Kembrovskaya, L M Tomil'chik, "Walter Ritz as a theoretical physicist and his research on the theory of atomic spectra", PHYS-USP, 1995, 38 (4), 435–455 This principle, the Rydberg–Ritz combination principle, is used today in identifying the transition lines of atoms.


References


External links

* {{DEFAULTSORT:Rydberg-Ritz Combination Principle Emission spectroscopy