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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.
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.
For a hydrogen atom, the role of reduced mass is most simply seen in the Bohr model of the atom, where the reduced mass appears in a simple calculation of the Rydberg constant and Rydberg equation, but the reduced mass also appears in the Schrödinger equation, and the Dirac equation for calculating atomic energy levels.
The ground state energy level of the electron in a hydrogen atom is −13.6 eV, [28] equivalent to an ultraviolet photon of roughly 91 nm wavelength. [ 29 ] The energy levels of hydrogen can be calculated fairly accurately using the Bohr model of the atom, in which the electron "orbits" the proton, like how Earth orbits the Sun.
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]
Deuterium, 2 H (atomic mass 2.014 101 777 844 (15) Da), the other stable hydrogen isotope, has one proton and one neutron in its nucleus, called a deuteron. 2 H comprises 26–184 ppm (by population, not mass) of hydrogen on Earth; the lower number tends to be found in hydrogen gas and higher enrichment (150 ppm) is typical of seawater.
An even number of protons or neutrons is more stable (higher binding energy) because of pairing effects, so even–even nuclides are much more stable than odd–odd. One effect is that there are few stable odd–odd nuclides: in fact only five are stable, with another four having half-lives longer than a billion years. [citation needed]