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Assume there is one electron in a given atomic orbital in a hydrogen-like atom (ion). The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus. The energy levels of an electron around a nucleus are given by:
Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. (Image not to scale) A hydrogen atom is an atom of the chemical element hydrogen.The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb force.
The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). [1]
An external-time energy–time uncertainty principle might say that measuring the energy of a quantum system to an accuracy requires a time interval > /. [38] However, Yakir Aharonov and David Bohm [ 46 ] [ 36 ] have shown that, in some quantum systems, energy can be measured accurately within an arbitrarily short time: external-time ...
A depiction of a hydrogen atom with size of central proton shown, and the atomic diameter shown as about twice the Bohr model radius (image not to scale) The ground state energy level of the electron in a hydrogen atom is −13.6 eV, [24] equivalent to an ultraviolet photon of roughly 91 nm wavelength. [25]
This was a significant step in the development of quantum mechanics. It also described the possibility of atomic energy levels being split by a magnetic field (called the Zeeman effect). Walther Kossel worked with Bohr and Sommerfeld on the Bohr–Sommerfeld model of the atom introducing two electrons in the first shell and eight in the second. [8]
Positronium is an "atom" consisting of an electron and a positron. Whereas the calculation of the energy levels of ordinary hydrogen is contaminated by theoretical uncertainties from the proton's internal structure, the particles that make up positronium have no internal structure so precise theoretical calculations can be performed.
Each energy level, or electron shell, or orbit, is designated by an integer, n as shown in the figure. The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory.