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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.
Rydberg was trying: = (+ ′) when he became aware of Balmer's formula for the hydrogen spectrum = In this equation, m is an integer and h is a constant (not to be confused with the later Planck constant). Rydberg therefore rewrote Balmer's formula in terms of wavenumbers, as =.
The spectral series of hydrogen, on a logarithmic scale. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom.
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]
Where R H is the same Rydberg constant for hydrogen from Rydberg's long known formula. This also means that the inverse of the Rydberg constant is equal to the Lyman limit. For the connection between Bohr, Rydberg, and Lyman, one must replace m with 1 to obtain
The Rydberg constant R M for a hydrogen atom (one electron), R is given by = + /, where is the mass of the atomic nucleus. For hydrogen-1, the quantity /, is about 1/1836 (i.e. the electron-to-proton mass ratio). For deuterium and tritium, the ratios are about 1/3670 and 1/5497 respectively.
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It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as n 2 (the n = 137 state of hydrogen has an atomic radius ~1 μm) and the geometric cross-section as n 4. Thus, Rydberg atoms are extremely large, with loosely bound valence electrons, easily perturbed or ionized by collisions or external fields.