Rydberg formula

The Rydberg formula gives the wavenumbers or wavelengths of spectral lines produced when electrons change energy levels in hydrogen or hydrogen-like atoms.

Rydberg constant: A physical constant that sets the scale of hydrogenic spectral wavenumbers. It supplies the formula’s characteristic scale, with corrections for finite nuclear mass.
Wavenumber: The number of wave cycles per unit distance, commonly expressed in inverse centimeters in spectroscopy. The Rydberg equation is often written most simply as a difference in wavenumber.
Johannes Rydberg: A Swedish physicist who formulated a relation organizing the wavelengths of atomic spectral lines. His empirical formula gave the equation its name.
Balmer series: The visible hydrogen spectral series formed by transitions ending at principal quantum number two. It is the most familiar set of lines predicted by the formula.
Schrödinger equation: A wave equation governing the quantum state and energy of nonrelativistic systems. Solving it for a Coulomb-bound electron derives the levels underlying the formula.
Principal quantum number: An integer quantum number that labels an electron shell and helps determine its energy in a hydrogen-like atom. The two principal quantum numbers specify the initial and final levels in each transition.
Wavelength: The distance between corresponding points on successive cycles of a wave. Taking the reciprocal of the predicted wavenumber gives a line’s wavelength.
Johann Jakob Balmer: A Swiss mathematician who found a numerical formula for visible hydrogen spectral lines in 1885. The Balmer relation was the hydrogen-specific predecessor generalized by Rydberg.
Lyman series: The ultraviolet hydrogen spectral series formed by transitions ending at principal quantum number one. The same relation predicts its ultraviolet line positions.
Dirac equation: A relativistic quantum equation for spin-one-half particles such as electrons. Its hydrogen solutions add fine-structure effects absent from the basic formula.

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