Rydberg constant

Rydberg constant, (symbol R_∞ or R_Η ), fundamental constant of atomic physics that appears in the formulas developed (1890) by the Swedish physicist Johannes Rydberg, describing the wavelengths or frequencies of light in various series of related spectral lines, most notably those emitted by hydrogen atoms in the Balmer series. The value of this constant is based on the premise that the nucleus of the atom emitting light is exceedingly massive compared with a single orbiting electron (hence the infinity symbol ∞). The constant can be expressed as α²m_ec/2h, where α is the fine-structure constant, m_e is the mass of the electron, c is the speed of light, and h is Planck’s constant.

The value of the Rydberg constant R_∞ is 10,973,731.56816 per metre. When used in this form in the mathematical description of series of spectral lines, the result is the number of waves per unit length, or the wavenumbers. Multiplication by the speed of light yields the frequencies of the spectral lines.