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Rydberg's formula as it appears in a November 1888 record. In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements.The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen.
The Balmer equation predicts the four visible spectral lines of hydrogen with high accuracy. Balmer's equation inspired the Rydberg equation as a generalization of it, and this in turn led physicists to find the Lyman, Paschen, and Brackett series, which predicted other spectral lines of hydrogen found outside the visible spectrum.
The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2. Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen. [10]
Three years later, the Swedish physicist Johannes Rydberg presented a generalized and more intuitive version of Balmer's formula that came to be known as the Rydberg formula. This formula indicated the existence of an infinite series of ever more closely spaced discrete energy levels converging on a finite limit. [6]
The hydrogen spectral series can be expressed simply in terms of the Rydberg constant for hydrogen and the Rydberg formula. In atomic physics, Rydberg unit of energy, symbol Ry, corresponds to the energy of the photon whose wavenumber is the Rydberg constant, i.e. the ionization energy of the hydrogen atom in a simplified Bohr model.
Next, Bohr was told by his friend, Hans Hansen, that the Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885 that described wavelengths of some spectral lines of hydrogen. [18] [22] This was further generalized by Johannes Rydberg in 1888, resulting in what is now known as the Rydberg ...
Within five years Johannes Rydberg came up with an empirical formula that solved the problem, presented first in 1888 and final form in 1890. Rydberg managed to find a formula to match the known Balmer series emission lines, and also predicted those not yet discovered. Different versions of the Rydberg formula with different simple numbers were ...
Two of Balmer's colleagues, Hermann Wilhelm Vogel and William Huggins, were able to confirm the existence of other lines of the Balmer series in the spectrum of hydrogen in white stars. Balmer's formula was later found to be a special case of the Rydberg formula, devised by Johannes Rydberg in 1888: