One-electron system

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The one-electron system is usually an atom that is ionized to such an extent that it only has a single electron . In general, the term describes a stable system made up of any positively charged elementary particle and an electron.

The classic one-electron system is hydrogen . A single electron is bound to a proton via the Coulomb interaction . The two hydrogen isotopes, deuterium and tritium , together with their electron, also represent such a system. A more unusual variant, for example, is positronium , an electron bound to its antiparticle .

Hydrogen-like ions

In principle, all atoms can be converted into such a one-electron system by ionization, which is also called a hydrogen-like ion . As two-particle systems (consisting of atomic nucleus and electron) or one-electron systems, they are most accessible to a mathematical description.

The ionization of an atom until only a single electron is left is easier, the fewer electrons the atom has from the start. You just have to ionize helium , lithium twice, and so on. The energy required increases with the number of electrons or with the atomic number of the element .

In the case of hydrogen-like ions with heavy nuclei ( heavy ions ), very high binding energies and field strengths of up to approx. 10 18  V / m occur. The electron is so strongly bound here (over 100  keV ) that relativistic effects become relevant. These ions are generated in heavy ion accelerators or by means of an electron beam ion trap and are an important object of investigation in basic physical research . One of the leading German research institutes in this field is the GSI Helmholtz Center for Heavy Ion Research in Darmstadt.

Mathematical treatment

In the simplest case, the procedure is the same as in Bohr's atomic model and only the higher atomic number (and possibly the higher nuclear mass ) compared to hydrogen is taken into account.

Bohr's atomic model could first be checked on the spectrum of hydrogen, then on other one-electron systems. The additional electrons that influence the energies of the spectral lines are missing there, which was not covered by Bohr's model. The experimental determination of the Rydberg constant and its change as a function of the mass ratio of the two system components was carried out on one-electron systems.

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