Rydberg formula for any hydrogen-like element


The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements.Rydberg worked on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement. He plotted the wavenumbers (n) 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.

Related formulas


λv wavelength of electromagnetic radiation emitted in vacuum (m)
RRydberg constant
ZAtomic number (dimensionless)
n1Integer such that n1 < n2 (dimensionless)
n2Integer such that n2 > n1 (dimensionless)