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The Rydberg constant was one of the most precisely determined physical constants, with a relative standard uncertainty of 1.1 × 10 −12. [2] This precision constrains the values of the other physical constants that define it.
In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. [2]: v1:376 He noticed that lines came in series and he found that he could simplify his calculations 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.
where λ is the wavelength of the absorbed/emitted light and R H is the Rydberg constant for hydrogen. The Rydberg constant is seen to be equal to 4 / B in Balmer's formula, and this value, for an infinitely heavy nucleus, is 4 / 3.645 0682 × 10 −7 m = 10 973 731.57 m −1. [3]
Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.
Rydberg constant: 10 973 731.568 157 (12) m −1: 1.1 ... While the values of the physical constants are independent of the system of units in use, each uncertainty ...
The version of the Rydberg formula that generated the Lyman series was: [2] = (= +) where n is a natural number greater than or equal to 2 (i.e., n = 2, 3, 4, .... Therefore, the lines seen in the image above are the wavelengths corresponding to n = 2 on the right, to n → ∞ on the left.
Figure 2: Energy levels in atomic lithium showing the Rydberg series of the lowest 3 values of orbital angular momentum converging on the first ionization energy. A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number, n.
In a theoretical model of atom, which has a infinitely massive nucleus, the energy (in wavenumbers) of a transition can be calculated from Rydberg formula: ~ = (′), where and ′ are principal quantum numbers, and is Rydberg constant.