Atomic electron transition: Difference between revisions

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{{short description|Change of an electron between energy levels within an atom}}

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[[File:Bohr-atom-electron-to-jump.svg|thumb|228x228px|An electron in a [[Bohr model]] atom, moving from [[Quantum number|quantum level]] {{math|1=''n'' = 3}} to {{math|1=''n'' = 2}} and releasing a [[photon]]. The energy of an electron is determined by it'sits orbit around the atom. The n = 0 orbit, commonly referred to as the [[ground state]], has the lowest energy of all states in the system. ]]

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In [[atomic physics]] and [[chemistry]], an '''atomic electron transition''' (also called an atomic transition, or quantum jump) is an [[electron]] changing from one [[energy level]] to another within an [[atom]]<ref>Schombert, James. [http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html "Quantum physics"] University of Oregon Department of Physics</ref> or [[artificial atom]].<ref>{{Cite journal |arxiv = 1009.2969|bibcode = 2011PhRvL.106k0502V|title = Observation of Quantum Jumps in a Superconducting Artificial Atom|journal = Physical Review Letters|volume = 106|issue = 11|pages = 110502|last1 = Vijay|first1 = R|last2 = Slichter|first2 = D. H|last3 = Siddiqi|first3 = I|year = 2011|doi = 10.1103/PhysRevLett.106.110502|pmid = 21469850| s2cid=35070320 }}</ref> The time scale of a quantum jump has not been measured experimentally. However, the [[Franck–Condon principle]] binds the upper limit of this parameter to the order of attoseconds.<ref>{{Cite journal |last=de la Peña |first=L. |last2=Cetto |first2=A. M. |last3=Valdés-Hernández |first3=A. |date=2020-12-04 |title=How fast is a quantum jump? |url=https://www.sciencedirect.com/science/article/pii/S0375960120307477 |journal=Physics Letters A |volume=384 |issue=34 |pages=126880 |doi=10.1016/j.physleta.2020.126880 |issn=0375-9601|arxiv=2009.02426 }}</ref>

Electrons jumping to energy levels of smaller n emit [[electromagnetic radiation]] in the form of a photon. Electrons can also absorb passing photons, which drives a quantum jump to a level of higher n. The larger the energy separation between the electron's initial and final state, the shorter the photons' [[wavelength]].<ref name=":0" />

== History ==

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publisher=Oxford University Press|isbn=978-0-19-850696-6}}</ref> Note that the actual phase is <math> (\omega t - \textbf{k} \cdot \textbf{r}) </math>. However, in many cases, the variation of <math> \textbf{k} \cdot \textbf{r} </math> is small over the atom (or equivalently, the radiation wavelength is much greater than the size of an atom) and this term can be ignored. This is called the dipole approximation. The atom can also interact with the oscillating magnetic field produced by the radiation, although much more weakly.

The Hamiltonian for this interaction, analogous to the energy of a classical dipole in aan electric field, is <math> H_I = e \textbf{r} \cdot \textbf{E}(t) </math>. The stimulated transition rate can be calculated using [[time-dependent perturbation theory]]; however, the result can be summarized using [[Fermi's golden rule]]:

<math display="block">

Rate \propto |eE_0|^2 \times | \lang 2 |