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 for the
hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb for ...
and the
alkali metal
The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, ''natrium'' and ''kalium''; these are still the origins of the names ...
s. The principle states that the
spectral lines
A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
of any element include
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
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 (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...
or reciprocal
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
, 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
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb for ...
, 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 was ...
:
where
is the wavelength,
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 ...
, and
and
are positive integers such that
. This is the difference of two terms of form
.
[
The exact Ritz Combination formula was mathematically derived from this where:
:
:
Where:
is the wavenumber,
is the limit of the series,
is a universal constant, (now known as ''R'')
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 particles that can ...
s whose energy ''E'' is proportional to the frequency and wavenumber of the light: (where ''h'' is the Planck constant, ''c'' is the speed of light, and 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 theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...
in 1913, an atom can have only certain energy levels
A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical pa ...
. 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 particles that can ...
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 atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word ''symbol'' suggests otherwise, it represents an actual ''valu ...
s which indicate their quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
s.
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: .
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 a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
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 hydrogen spectral series, six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empiri ...
. 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 was ...
. 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
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{{DEFAULTSORT:Rydberg-Ritz Combination Principle
Emission spectroscopy
Old quantum theory