- Rydberg constant
The

**Rydberg**, named after the Swedishconstant physicist Johannes Rydberg , is aphysical constant relating to atomic spectra in the science ofspectroscopy . Rydberg initially determind its value empirically from spectroscopy, but then later, it was found that its value could be calculated from more-fundamental constants by usingquantum mechanics .The "Rydberg constant" represents the limiting value of the highest

wavenumber (the inverse wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing the hydrogen atom from its ground state. The spectrum of hydrogen can be expressed simply in terms of the Rydberg constant, using theRydberg formula .**Value of the Rydberg constant**Making use of the simplifying assumption that the mass of the atomic nucleus is infinite compared to the mass of the electron, the Rydberg constant is (according to 2002

CODATA results)::$R\_infty\; =\; frac\{m\_e\; e^4\}\{8\; epsilon\_0^2\; h^3\; c\}\; =\; 1.0973731568525(73)\; imes\; 10^7\; ,mathrm\{m\}^\{-1\}$::where,::: $h$ is the

Planck's constant ,::: $m\_e$ is therest mass of theelectron ,::: $e$ is theelementary charge ,::: $c$ is thespeed of light invacuum , and::: $epsilon\_0$ is thepermittivity of free space .This constant is often used in

atomic physics in the form of an energy::$h\; c\; R\_infty\; =\; 13.6056923(12)\; ,mathrm\{eV\}\; equiv\; 1\; ,mathrm\{Ry\}$Two complications arise. One is that one may wish to discuss a hydrogenlike ion, i.e., an atom with atomic number Z that has only one electron. In this case, the wavenumbers and photon energies are scaled up by a factor of $Z^2$. The other is that the mass of the atomic nucleus is not actually infinite compared to the mass of the electron. The predicted spectrum must then be corrected by substituting the

reduced mass for the mass of the electron, resulting in::$R\_M\; =\; frac\{R\_infty\}\{1+m\_e/M\}$::where,:::$R\_M$ is the Rydberg constant for a certain

atom with oneelectron with therest mass $m\_e$:::$M$ is the mass of the atomic nucleus.The Rydberg constant is one of the most well-determined physical constants, with a relative experimental uncertainty of less than 7 parts per trillion. The ability to measure it directly to such a high precision constrains the proportions of the values of the other physical constants that define it.

**Alternate expressions**The Rydberg constant can also be expressed as the following equations.

:$R\_infty\; =\; frac\{alpha^2\; m\_e\; c\}\{4\; pi\; hbar\}\; =\; frac\{alpha^2\}\{2\; lambda\_e\}$and:$h\; c\; R\_infty\; =\; frac\{h\; c\; alpha^2\}\{2\; lambda\_e\}\; =\; frac\{h\; f\_C\; alpha^2\}\{2\}\; =\; frac\{hbar\; omega\_C\}\{2\}\; alpha^2$where:: $h$ is

Planck's constant ,:: $c$ is thespeed of light in a vacuum,:: $alpha$ is thefine-structure constant ,:: $lambda\_e$ is theCompton wavelength of the electron,:: $f\_C$ is the Compton frequency of the electron,:: $hbar$ is the reducedPlanck's constant , and:: $omega\_C$ is the Compton angular frequency of the electron.**The Derivation of Rydberg constant from quantum mechanics**Historically, the Rydberg equation was found "empirically" (experimentally), and it predated the development of quantum theory. To understand its significance in terms of the quantum theory, we can start from the equation

: $E\_mathrm\{total\}\; =\; frac\{-\; m\_e\; e^4\}\{8\; epsilon\_0^2\; h^2\}.\; frac\{1\}\{n^2\}$

for the energy of the electron in the nth energy state, as can be derived either from the

Bohr model or from a fully quantum-mechanical treatment of the hydrogen atom. Therefore a change in energy in an electron changing from one value of $n$ to another is: $Delta\; E\; =\; frac\{\; m\_e\; e^4\}\{8\; epsilon\_0^2\; h^2\}\; left(\; frac\{1\}\{n\_mathrm\{initial\}^2\}\; -\; frac\{1\}\{n\_mathrm\{final\}^2\}\; ight)$

We simply change the units to wavelength $left(\; frac\{1\}\{\; lambda\}\; =\; frac\; \{E\}\{hc\}\; ightarrow\; Delta\{E\}\; =\; hc\; Delta\; left(\; frac\{1\}\{lambda\}\; ight)\; ight)$ and we get

: $Delta\; left(\; frac\{1\}\{\; lambda\}\; ight)\; =\; frac\{\; m\_e\; e^4\}\{8\; epsilon\_0^2\; h^3\; c\}\; left(\; frac\{1\}\{n\_mathrm\{initial\}^2\}\; -\; frac\{1\}\{n\_mathrm\{final\}^2\}\; ight)$

where:: $h$ is

Planck's constant ,:: $m\_e$ is therest mass of theelectron ,:: $e$ is theelementary charge ,:: $c$ is thespeed of light invacuum , and:: $epsilon\_0$ is thepermittivity of free space .:: $n\_mathrm\{initial\}$ and $n\_mathrm\{final\}$ being the electron shell number of the hydrogen atomWe have therefore found the Rydberg constant for hydrogen to be: $R\_H\; =\; frac\{\; m\_e\; e^4\}\{8\; epsilon\_0^2\; h^3\; c\}$

**ee also***

Rydberg formula **References*** [

*http://physics.nist.gov/cuu/Constants/codata.pdf CODATA recommendations 2006*]

* [*http://scienceworld.wolfram.com/physics/Rydberg.html Mathworld*]

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### Look at other dictionaries:

**Rydberg constant**— ▪ physics (symbol R∞), fundamental constant of atomic physics that appears in the formulas developed (1890) by the Swedish physicist J. R. Rydberg (Rydberg, Johannes Robert), describing the wavelengths or frequencies of light in various… … Universalium**Rydberg constant**— Rydbergo konstanta statusas T sritis Standartizacija ir metrologija apibrėžtis Apibrėžtį žr. priede. priedas( ai) Grafinis formatas atitikmenys: angl. Rydberg constant vok. Rydberg Konstante, f rus. константа Ридберга, f; постоянная Ридберга, f… … Penkiakalbis aiškinamasis metrologijos terminų žodynas**Rydberg constant**— Rydbergo konstanta statusas T sritis fizika atitikmenys: angl. Rydberg constant vok. Rydberg Konstante, f; Rydbergsche Konstante, f rus. постоянная Ридберга, f pranc. constante de Rydberg, f … Fizikos terminų žodynas**rydberg constant**— noun a wave number characteristic of the wave spectrum of each element • Syn: ↑rydberg, ↑rydberg unit • Hypernyms: ↑wave number … Useful english dictionary**Rydberg constant**— noun a universal scaling factor for all spectroscopic transitions … Wiktionary**Rydberg**— can refer to: * Rydberg (crater), a crater on the moon *In physics, ** Rydberg constant **Rydberg formula **Rydberg atom (an atom in a state of high principal quantum number) **a unit of energy, derived from the Rydberg constant, equal to half… … Wikipedia**Rydberg formula**— The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. The formula was invented by the Swedish physicist Johannes Rydberg and presented on November 5, 1888.HistoryIn the 1880s,… … Wikipedia**Rydberg, Johannes Robert**— ▪ Swedish physicist born Nov. 8, 1854, Halmstad, Swed. died Dec. 28, 1919, Lund Swedish physicist for whom the Rydberg constant in spectroscopy is named. Educated at the University of Lund, Rydberg received his bachelor s degree in… … Universalium**rydberg unit**— noun a wave number characteristic of the wave spectrum of each element • Syn: ↑rydberg, ↑rydberg constant • Hypernyms: ↑wave number * * * noun see rydberg constant … Useful english dictionary**Rydberg-Konstante**— Rydbergo konstanta statusas T sritis Standartizacija ir metrologija apibrėžtis Apibrėžtį žr. priede. priedas( ai) Grafinis formatas atitikmenys: angl. Rydberg constant vok. Rydberg Konstante, f rus. константа Ридберга, f; постоянная Ридберга, f… … Penkiakalbis aiškinamasis metrologijos terminų žodynas