The Rydberg formula (Rydberg-Ritz formula) is used in atomic physics for determining the full spectrum of light emission from hydrogen, later extended to be useful with any element by use of the Rydberg-Ritz combination principle. Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... Legend: γ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves: EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultra high frequency VHF = Very high frequency HF = High... This page is a list of sources of light. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... The periodic table of the chemical elements A chemical element, often called simply an element, is a substance that cannot be decomposed or transformed into other chemical substances by ordinary chemical processes. ... It has been suggested that this article or section be merged with Ritz method. ...

A piece of the original document detailing the Rydberg formula in 1888.

The spectrum is the set of wavelengths of photons emitted when electrons jump between discrete energy levels, "shells" around the atom of a certain chemical element. This discovery was later to provide motivation for the creation of quantum physics. Image File history File links A piece of the original document detailing the Rydberg formula, used by permission. ... The wavelength is the distance between repeating units of a wave pattern. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, microwaves, radio waves, and visible light are all forms of light. ... The electron is a fundamental subatomic particle that carries an electric charge. ... Look up discrete in Wiktionary, the free dictionary. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle of a chemical element that retains its chemical properties. ... The periodic table of the chemical elements A chemical element, often called simply an element, is a substance that cannot be decomposed or transformed into other chemical substances by ordinary chemical processes. ... Fig. ...

The formula was invented by the Swedish physicist Johannes Rydberg and presented on November 5, 1888. ... Janne Rydberg Johannes Robert Rydberg, commonly known as Janne Rydberg, (November 8, 1854 - December 28, 1919), was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to predict the wavelengths of photons (of light and other electromagnetic radiation) emitted by changes in the energy... November 5 is the 309th day of the year (310th in leap years) in the Gregorian Calendar, with 56 days remaining. ... 1888 (MDCCCLXXXVIII) is a leap year starting on Sunday (click on link for calendar) of the Gregorian calendar or a leap year starting on Tuesday of the Julian calendar. ...

History

By 1890, Rydberg had discovered a formula describing the relation between the wavelengths in spectral lines of alkali metals, and also found that the 1885 Balmer's formula for the visible lines of hydrogen was a special case of a more general law. In atomic physics, the Balmer series is the designation of one of a set of six different named series describing the spectral line emissions of the hydrogen atom. ...

Specifically, Rydberg found that he could simplify his calculations by using the wavenumber (the number of waves occupying a set unit of length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement. He plotted the wavenumbers of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted. Wavenumber in most physical sciences is a wave property inversely related to wavelength, having units of inverse length. ... The wavelength is the distance between repeating units of a wave pattern. ...

Although the Rydberg formula was later found to be imprecise for most spectral lines of atoms of higher atomic number than hydrogen, it was found to be quite precise for hydrogen, generating not only the Balmer series in the visible spectrum, but also other series of lines in the ultraviolet and infrared. By 1906, Theodore Lyman had begun to analyze the hydrogen Lyman series of wavelengths in the ultraviolet spectrum named for him, that were already known to fit the Rydberg formula. Other hydrogen line-series in the infrared, named for other discoverers, are described below. All are described by the Rydberg equation. In chemistry and physics, the atomic number (Z) is the number of protons found in the nucleus of an atom. ... Two of the balmer lines (α and β) are clearly visible in this emission spectrum of a deuterium lamp. ... Theodore Lyman (1874 - 1954) was a U.S. physicist and spectroscopist. ... The Lyman series is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number referring to the energy level of the electron). ...

Besides describing the hydrogen series spectral lines, the Rydberg equation also describes alkali metal atoms with a single valence electron orbiting well clear of the inner electron core. It also generates correct values for K-alpha (K_α) spectral lines in all elements, with modification as described by Moseley's law. Moseleys law is an empirical law concerning the characteristic electromagnetic spectrum that is emitted or absorbed by atoms. ...

Expressing results in terms of wavenumber was the key to Rydberg's discovery, but the fundamental reason for this was not discovered for another 15 years. Light wavenumber is proportional to frequency (1/λ = frequency/c), and therefore also proportional to light quantum energy E. Thus, 1/λ = (h/c)E. Modern understanding is that Rydberg's plots were simplified because of the underlying simplicity of the behavior of spectral lines, in terms of fixed (quantized) energy differences between electron orbitals in atoms. This phenomenon was first understood by Niels Bohr in 1913, as incorporated in the Bohr model of the atom. Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics. ... The Bohr model of the hydrogen atom. ...

Rydberg formula for hydrogen

Where

λ_vac is the wavelength of the light emitted in vacuum,

R_H is the Rydberg constant for hydrogen,

n₁ and n₂ are integers such that n₁ < n₂,

Z is the atomic number, which is 1 for hydrogen.

By setting n₁ to 1 and letting n₂ run from 2 to infinity, the spectral lines known as the Lyman series converging to 91nm are obtained, in the same manner: The wavelength is the distance between repeating units of a wave pattern. ... Look up Vacuum in Wiktionary, the free dictionary. ... The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ã…ngström and Johann Balmer. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... The Lyman series is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number referring to the energy level of the electron). ...

n1	n2	Name	Converge toward
1		Lyman series	91nm
2		Balmer series	365nm
3		Paschen series	821nm
4		Brackett series	1459nm
5		Pfund series	2280nm
6		Humphreys series	3283nm

The Lyman series is in the ultraviolet while the Balmer series is in the visible and the Paschen, Brackett, Pfund, and Humphreys series are in the infrared. The Lyman series is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n is the principal quantum number referring to the energy level of the electron). ... Two of the balmer lines (α and β) are clearly visible in this emission spectrum of a deuterium lamp. ... The Paschen series is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 4 to n = 3 (where n refers to the energy level of the electron). ... The Brackett series is a series of absorption or emission lines that are due to electron transitions between the fourth and higher energy levels of the hydrogen atom. ... This article may be too technical for most readers to understand. ... In atomic physics, the Humphreys series is the designation of one of a set of six different named series describing the spectral line emissions of the hydrogen atom, and was discovered by Curtis J. Humphreys in 1953. ...

Rydberg formula for any hydrogen-like element

The formula above can be extended for use with any hydrogen-like chemical elements. The periodic table of the chemical elements A chemical element, often called simply an element, is a substance that cannot be decomposed or transformed into other chemical substances by ordinary chemical processes. ...

where

is the wavelength of the light emitted in vacuum;

is the Rydberg constant for this element;

is the atomic number, i.e. the number of protons in the atomic nucleus of this element;

and are integers such that .

It's important to notice that this formula can be applied only to hydrogen-like, also called hydrogenic atoms of chemical elements, i.e. atoms with only one electron being affected by an easy-to-estimate effective nuclear charge. Examples would include He⁺¹, Li²⁺, Be³⁺ etc., where no other electrons exist in the atom. The wavelength is the distance between repeating units of a wave pattern. ... Look up Vacuum in Wiktionary, the free dictionary. ... The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ã…ngström and Johann Balmer. ... In chemistry and physics, the atomic number (Z) is the number of protons found in the nucleus of an atom. ... // For alternative meanings see proton (disambiguation). ... A semi-accurate depiction of the helium atom. ... The periodic table of the chemical elements A chemical element, often called simply an element, is a substance that cannot be decomposed or transformed into other chemical substances by ordinary chemical processes. ...

The Rydberg formula provides correct wavelengths for extremely distant electrons, where the effective nuclear charge can be estimated as the same as that for hydrogen, since all but one of the nuclear charges have been screened by other electrons, and the core of the atom has an effective positive charge of +1.

Finally, with certain modifications (replacement of Z by Z-1, and use of the integers 1 and 2 for the n's to give a numerical value of 3/4 for the difference of their inverse squares), the Rydberg formula provides correct values in the special case of K-alpha lines, since the transition in question is the K-alpha transition of the electron from the 1s orbital to the 2p orbital. This is analogous to the Lyman-alpha line transition for hydrogen, and has the same frequency factor. Because the 2p electron is not screened by any other electrons in the atom from the nucleus, the nuclear charge is diminished only by the single remaining 1s electron, causing the system to be effectively a hydrogenic atom, but with a diminished nuclear charge Z-1. Its frequency is thus the Lyman-alpha hydrogen frequency, increased by a factor of (Z-1)². This formula of f = c/λ = Lyman-alpha frequency * (Z-1)² is historically known as Moseley's law (having added a factor c to convert wavelength to frequency), and can be used to predict wavelengths of the K_α (K-alpha) X-ray spectral emission lines of chemical elements from aluminum to gold. See the biography of Henry Moseley for the historical importance of this law, which was derived empirically at about the same time it was explained by the Bohr model of the atom. The Lyman-alpha line is a spectral line of hydrogen in the Lyman series, emitted when the electron falls from the n=2 orbit to the n=1 orbit. ... Moseleys law is an empirical law concerning the characteristic electromagnetic spectrum that is emitted or absorbed by atoms. ... Henry Moseley at work. ... The Bohr model of the hydrogen atom. ...

For other spectral transitions in multi-electron atoms, the Rydberg formula generally provides incorrect results, since the magnitude of the screening of inner electrons for outer-electron transitions, is variable and not possible to compensate for in the simple manner above.

References

Mike Sutton, “Getting the numbers right – the lonely struggle of Rydberg” Chemistry World, Vol. 1, No. 7, July 2004.

See also

• Rydberg-Ritz combination principle
• Balmer's Constant
• Hydrogen line