Rydberg constant

The Rydberg constant $R_\infty$ is a natural constant named after Johannes Rydberg. It occurs in the Rydberg formula, an approximate formula for calculating atomic spectra. Its value is the ionization energy of the hydrogen atom expressed as a wave number, neglecting relativistic effects and the co-motion of the nucleus (i.e. at infinite nuclear mass, hence the index $\infty$ ).

The current recommended value of the Rydberg constant is:

$R_{\infty }=10\,973\,731{,}568\,160(21)\,\mathrm {m} ^{-1}.$

The relative standard uncertainty is 1.9 - 10-12, making it the most accurately measured natural constant of all.

Relationship with other constants of nature

The Rydberg constant is obtained from the fine structure constant α and the Compton wavelength λC_{,e of} an electron according to

$R_{\infty }={\frac {\alpha ^{2}}{2}}\,{\frac {1}{\lambda _{\mathrm {C,e} }}}={\frac {\alpha ^{2}}{2}}\,{\frac {m_{\mathrm {e} }c}{h}}={\frac {m_{\mathrm {e} }e^{4}}{8c\varepsilon _{0}^{2}h^{3}}}$

with

$m_{{\mathrm e}}$ the mass of the electron
the speed of light
the Planck quantum of action
of the elementary charge
$\varepsilon _{0}$ of the electric field constant.

Rydberg frequency and Rydberg energy

The Rydberg constant is also often expressed as frequency or as energy. The recommended values are:

Rydberg frequency: $R=c\,R_{\infty }=3{,}289\,841\,960\,2508(64)\cdot 10^{15}\,\mathrm {Hz}$
Rydberg energy: $R_{y}=h\,R=h\,c\,R_{\infty }=2{,}1798723611035(42)\cdot 10^{-18}\,\mathrm {J} =13{,}605\,693\,122\,994(26)\,\mathrm {eV} =1\,\mathrm {Ry} .$

The concrete value of the Rydberg energy R_y is called a Rydberg; thus the Rydberg becomes usable as a unit of measure for energies.

Questions and Answers

Q: What is the Rydberg constant?

A: The Rydberg constant is a physical constant relating to the electromagnetic spectra of an atom. It is used to express the limiting value of the highest wavenumber (inverse wavelength) of any photon that can be emitted from an atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing an atom from its ground state.

Q: Who was it named after?

A: The Rydberg constant was named after Swedish physicist Johannes Rydberg.

Q: What symbols are used for it?

A: The symbol for heavy atoms is R∞ and for hydrogen it is RH.

Q: How was its value calculated?

A: Its value was calculated from more fundamental constants via Niels Bohr's Bohr model.

Q: What are some applications of this constant?

A: This constant can be used to express the hydrogen spectral series in terms of the Rydberg formula, and also corresponds to energy of a photon whose wavenumber is equal to this constant - i.e., ionization energy of a hydrogen atom.

Q: Is it one of most accurately measured physical constants as of 2018?

A: Yes, as of 2018, both R∞ and electron spin g-factor are two most accurately measured physical constants.