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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.
This choice also places K-alpha firmly in the X-ray energy range. Similarly to Lyman-alpha, the K-alpha emission is composed of two spectral lines, K-alpha 1 (Kα 1) and K-alpha 2 (Kα 2). [6] The K-alpha 1 emission is slightly higher in energy (and, thus, has a lower wavelength) than the K-alpha 2 emission.
The higher the temperature of the gas, the wider the distribution of velocities in the gas. Since the spectral line is a combination of all of the emitted radiation, the higher the temperature of the gas, the broader the spectral line emitted from that gas. This broadening effect is described by a Gaussian profile and there is no associated shift.
According to Planck's distribution law, the spectral energy density (energy per unit volume per unit frequency) at given temperature is given by: [4] [5] (,) = alternatively, the law can be expressed for the spectral radiance of a body for frequency ν at absolute temperature T given as: [6] [7] [8] (,) = where k B is the Boltzmann ...
Following Bohr's lead, Moseley found that for the spectral lines, this relationship could be approximated by a simple formula, later called Moseley's Law. [2] = where: is the frequency of the observed X-ray emission line
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.
To be accurate, the above equations need to be multiplied by the (normalized) spectral line shape, in which case the units will change to include a 1/Hz term. Under conditions of thermodynamic equilibrium, the number densities n 2 {\displaystyle n_{2}} and n 1 {\displaystyle n_{1}} , the Einstein coefficients, and the spectral energy density ...
However, a more accurate model takes into account relativistic and spin effects, which break the degeneracy of the energy levels and split the spectral lines. The scale of the fine structure splitting relative to the gross structure energies is on the order of ( Zα ) 2 , where Z is the atomic number and α is the fine-structure constant , a ...