Atomic electron transition: Difference between revisions

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

[[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. ]]

{{About||the TV series|Quantum Leap|the sculpture|The Quantum Leap}}

[[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's 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. ]]

{{Use mdy dates|date=February 2016}}

In [[atomic physics]] and [[chemistry]], an '''atomic electron transition''' (also called an atomic transition, quantum jump, or quantum jumpleap) 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 [[Attosecond|attoseconds]].<ref>{{Cite journal |lastlast1=de la Peña |firstfirst1=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 |bibcode=2020PhLA..38426880D }}</ref>

Electrons jumpingcan to''relax'' energyinto levelsstates of smallerlower energy nby emitemitting [[electromagnetic radiation]] in the form of a photon. Electrons can also absorb passing photons, which drives''excites'' athe quantumelectron jump tointo a levelstate of higher nenergy. The larger the energy separation between the electron's initial and final state, the shorter the photons' [[wavelength]].<ref name=":0" />

== History ==

Danish physicist [[Niels Bohr]] first theorized that electrons can perform quantum jumps in 1913.<ref>{{Cite news|last=Gleick|first=James|date=1986-10-21|title=PHYSICISTS FINALLY GET TO SEE QUANTUM JUMP WITH OWN EYES|language=en-US|work=The New York Times|url=https://www.nytimes.com/1986/10/21/science/physicists-finally-get-to-see-quantum-jump-with-own-eyes.html|access-date=2021-12-06|issn=0362-4331}}</ref> Soon after, [[James Franck]] and [[Gustav Ludwig Hertz]] [[Franck–Hertz experiment|proved experimentally]] that atoms have quantized energy states.<ref>{{Cite web|title=Franck-Hertz experiment {{!}} physics {{!}} Britannica|url=https://www.britannica.com/science/Franck-Hertz-experiment|access-date=2021-12-06|website=www.britannica.com|language=en}}</ref>

The observability of quantum jumps was predicted by [[Hans Dehmelt]] in 1975, and they were first observed using [[Quadrupole ion trap|trapped ions]] of [[barium]] at [[University of Hamburg]] and [[Mercury (element)|mercury]] at [[NIST]] in 1986.<ref name=":0">{{cite journal|last1=Itano|first1=W. M.|last2=Bergquist|first2=J. C.|last3=Wineland|first3=D. J.|date=2015|title=Early observations of macroscopic quantum jumps in single atoms|url=http://tf.boulder.nist.gov/general/pdf/2723.pdf|journal=International Journal of Mass Spectrometry|volume=377|page=403|bibcode=2015IJMSp.377..403I|doi=10.1016/j.ijms.2014.07.005}}</ref>

== Theory ==

An atom interacts with the oscillating [[electric field]]:

{{NumBlk|:|<math> E(t) = |\textbf{E}_0| Re( e^{-i{\omega}t} \hat{\textbf{e}}_\mathrm{rad} )</math>|{{EquationRef|1}}}}

with amplitude <math>|\textbf{E}_0|</math>, angular frequency <math>\omega</math>, and polarization vector <math>\hat{\textbf{e}}_\mathrm{rad}</math>.<ref>{{Cite book|title=Atomic Physics|author=Foot, CJ|year=2004|

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 |

\textbf{r} \cdot \hat{\textbf{e}}_\mathrm{rad} |1 \rang |^2

</math>

The dipole matrix element can be decomposed into the product of the radial integral and the angular integral. The angular integral is zero unless the [[selection rules]] for the atomic transition are satisfied.