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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.
The wavelength will always be positive because n′ is defined as the lower level and so is less than n. This equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by Z = 1.
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.
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.
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.
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]
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.
An electron falling from energy state 3 to energy state 2 (left) emits a photon. The wavelength is given by the Rydberg formula (middle). Calculating the wavelength for hydrogen energy levels, it correspond to a red photon (right). The important question was what will be the intensity of radiation in the spectrum at that wavelength?
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