Editing Electron (section)

== History ==
{{See also|History of electromagnetic theory|label 1=History of electromagnetism}}

=== Identification ===

In 1838, British natural philosopher [[Richard Laming]] first hypothesized the concept of an indivisible quantity of electric charge to explain the [[Chemical property|chemical properties]] of atoms.<ref name="arabatzis" /> Irish physicist [[George Johnstone Stoney]] named this charge "electron" in 1891, and [[J. J. Thomson]] and his team of British physicists identified it as a particle in 1897 during the [[cathode ray|cathode-ray tube experiment]].<ref name="thomson" /> 

=== Discovery of effect of electric force ===
The [[Ancient Greece#Science and technology|ancient Greeks]] noticed that [[amber]] attracted small objects when rubbed with fur. Along with [[lightning]], this phenomenon is one of humanity's earliest recorded experiences with [[Electricity#History|electricity]].<ref name="DictOrigins" /> In his 1600 treatise {{lang|la|[[De Magnete]]}}, the English scientist [[William Gilbert (astronomer)|William Gilbert]] coined the [[Neo-Latin]] term {{lang|la|electrica}}, to refer to those substances with property similar to that of amber which attract small objects after being rubbed.<ref name=Benjamin>
{{citation
 | last=Benjamin
 | first=Park
 | title=A history of electricity (The intellectual rise in electricity) from antiquity to the days of Benjamin Franklin
 | place=New York
 | publisher=J. Wiley
 | year=1898
 | pages=315, 484–5
 | url=https://archive.org/details/cu31924004128686/page/n10
 | isbn=978-1-313-10605-4
}}</ref> Both ''electric'' and ''electricity'' are derived from the Latin ''{{lang|la|ēlectrum}}'' (also the root of the [[electrum|alloy of the same name]]), which came from the [[Ancient Greek|Greek]] word for amber, {{lang|grc|ἤλεκτρον}} (''{{lang|grc-Latn|ēlektron}}'').

=== Discovery of two kinds of charges ===
In the early 1700s, French chemist [[Charles François de Cisternay du Fay|Charles François du Fay]] found that if a charged gold-leaf is repulsed by glass rubbed with silk, then the same charged gold-leaf is attracted by amber rubbed with wool. From this and other results of similar types of experiments, du Fay concluded that electricity consists of two [[Aether theories|electrical fluids]], ''vitreous'' fluid from glass rubbed with silk and ''resinous'' fluid from amber rubbed with wool.  These two fluids can neutralize each other when combined.<ref name=Benjamin /><ref>
{{cite book
 | last = Keithley
 | first = J.F.
 | year = 1999
 | title = The Story of Electrical and Magnetic Measurements: From 500 B.C. to the 1940s
 | url = https://books.google.com/books?id=uwgNAtqSHuQC&pg=PR7
 | publisher = [[IEEE|IEEE Press]]
 | pages = 19–20
 | isbn = 978-0-7803-1193-0
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082420/https://books.google.com/books?id=uwgNAtqSHuQC&pg=PR7
 | url-status = live
}}</ref> American scientist [[Ebenezer Kinnersley]] later also independently reached the same conclusion.<ref name="Cajori1917">
{{cite book
 |first=Florian |last=Cajori
 |title=A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories
 |url=https://archive.org/details/historyofphysics00cajo
 |year=1917 |publisher=Macmillan
}}</ref>{{rp|118}} A decade later [[Benjamin Franklin]] proposed that electricity was not from different types of electrical fluid, but a single electrical fluid showing an excess (+) or deficit (−). He gave them the modern [[electric charge|charge]] nomenclature of positive and negative respectively.<ref>
{{cite web
 | title = Benjamin Franklin (1706–1790)
 | url = https://scienceworld.wolfram.com/biography/FranklinBenjamin.html
 | work = [[ScienceWorld|Eric Weisstein's World of Biography]]
 | publisher = [[Wolfram Research]]
 | access-date = 2010-12-16
 | df = dmy-all
 | archive-date = 2013-08-27
 | archive-url = https://web.archive.org/web/20130827114343/http://scienceworld.wolfram.com/biography/FranklinBenjamin.html
 | url-status = live
}}</ref> Franklin thought of the charge carrier as being positive, but he did not correctly identify which situation was a surplus of the charge carrier, and which situation was a deficit.<ref>
{{cite book
 |last1=Myers | first1 = R.L.
 | year = 2006
 | title = The Basics of Physics
 | url = https://archive.org/details/basicsofphysics0000myer/page/242
 |url-access=registration
 | publisher = [[Greenwood Publishing Group]]
 | page=242
 | isbn = 978-0-313-32857-2
}}</ref>

Between 1838 and 1851, British natural philosopher [[Richard Laming]] developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit [[electric charge]]s.<ref name="farrar">
{{cite journal
 | last = Farrar | first = W.V.
 | year = 1969
 | title = Richard Laming and the Coal-Gas Industry, with His Views on the Structure of Matter
 | journal = [[Annals of Science]]
 | volume = 25 | pages = 243–254
 | doi =10.1080/00033796900200141
 | issue = 3
}}</ref> Beginning in 1846, German physicist [[Wilhelm Eduard Weber]] theorized that electricity was composed of positively and negatively charged fluids, and their interaction was governed by the [[Inverse-square law|inverse square law]]. After studying the phenomenon of [[electrolysis]] in 1874, Irish physicist [[George Johnstone Stoney]] suggested that there existed a "single definite quantity of electricity", the charge of a [[Valence (chemistry)|monovalent]] [[ion]]. He was able to estimate the value of this elementary charge ''e'' by means of [[Faraday's laws of electrolysis]].<ref>
{{cite journal
 | last = Barrow | first = J.D.
 | year = 1983
 | title = Natural Units Before Planck
 | journal = [[Astronomy & Geophysics|Quarterly Journal of the Royal Astronomical Society]]
 | volume = 24 | pages = 24–26
 | bibcode = 1983QJRAS..24...24B
}}</ref> However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicist [[Hermann von Helmholtz]] argued that both positive and negative charges were divided into elementary parts, each of which "behaves like atoms of electricity".<ref name="arabatzis">
{{cite book
 | last = Arabatzis
 | first = T.
 | year = 2006
 | title = Representing Electrons: A Biographical Approach to Theoretical Entities
 | url = https://books.google.com/books?id=rZHT-chpLmAC&pg=PA70
 | pages = 70–74, 96
 | publisher = University of Chicago Press
 | isbn = 978-0-226-02421-9
 | access-date = 2020-08-25
 | archive-date = 2021-01-07
 | archive-url = https://web.archive.org/web/20210107160308/https://books.google.com/books?id=rZHT-chpLmAC&pg=PA70
 | url-status = live
}}</ref>

Stoney initially coined the term ''electrolion'' in 1881. Ten years later, he switched to ''electron'' to describe these elementary charges, writing in 1894: "...&nbsp;an estimate was made of the actual amount of this most remarkable fundamental unit of electricity, for which I have since ventured to suggest the name ''electron''". A 1906 proposal to change to ''electrion'' failed because [[Hendrik Lorentz]] preferred to keep ''electron''.<ref>
{{cite book
 | first=Sōgo
 | last=Okamura
 | title=History of Electron Tubes
 | url=https://books.google.com/books?id=VHFyngmO95YC&pg=PR11
 | access-date=29 May 2015
 | year=1994
 | publisher=IOS Press
 | isbn=978-90-5199-145-1
 | page=11
 | quote=In 1881, Stoney named this electromagnetic 'electrolion'. It came to be called 'electron' from 1891. [...] In 1906, the suggestion to call cathode ray particles 'electrions' was brought up but through the opinion of Lorentz of Holland 'electrons' came to be widely used.
 | archive-date=11 May 2016
 | archive-url=https://web.archive.org/web/20160511214552/https://books.google.com/books?id=VHFyngmO95YC&pg=PR11
 | url-status=live
}}</ref><ref name="GJStoney">
{{cite journal
 | last = Stoney
 | first = G.J.
 | year = 1894
 | title = Of the "Electron," or Atom of Electricity
 | journal = [[Philosophical Magazine]]
 | volume = 38
 | issue = 5
 | pages = 418–420
 | doi = 10.1080/14786449408620653
 | url = https://zenodo.org/record/1431209
 | access-date = 2019-08-25
 | archive-date = 2020-10-31
 | archive-url = https://web.archive.org/web/20201031080323/https://zenodo.org/record/1431209
 | url-status = live
}}</ref> The word ''electron'' is a combination of the words ''<u>electr</u>ic'' and ''i<u>on</u>''.<ref>"electron, n.2". OED Online. March 2013. Oxford University Press. Accessed 12 April 2013 [https://www.oed.com/view/Entry/60302?rskey=owKYbt&result=2] {{Webarchive|url=https://web.archive.org/web/20210427080603/https://www.oed.com/view/Entry/60302?rskey=owKYbt&result=2|date=2021-04-27}}</ref> The suffix [[wikt:-on|-''on'']] which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived from electron.<ref>
{{cite book
 | editor-last = Soukhanov | editor-first = A.H.
 | year = 1986
 | title = Word Mysteries & Histories
 | page = 73
 | publisher = Houghton Mifflin
 | isbn = 978-0-395-40265-8
}}</ref><ref>
{{cite book
 | editor-last = Guralnik | editor-first = D.B.
 | year = 1970
 | title = Webster's New World Dictionary
 | publisher = Prentice Hall
 | page = 450
}}</ref>

=== Discovery of free electrons outside matter ===
{{see also|Cathode ray|J. J. Thomson#Discovery of the electron}}

[[File:Cyclotron motion wider view.jpg|right|thumb|alt=A round glass vacuum tube with a glowing circular beam inside|A beam of electrons deflected by a magnetic field into a circle<ref>
{{cite book
 | last1 = Born
 | first1 = M.
 | last2 = Blin-Stoyle
 | first2 = R.J.
 | last3 = Radcliffe
 | first3 = J.M.
 | year = 1989
 | title = Atomic Physics
 | url = https://books.google.com/books?id=NmM-KujxMtoC&pg=PA26
 | page = 26
 | publisher = [[Courier Dover]]
 | isbn = 978-0-486-65984-8
 | access-date = 2020-08-25
 | archive-date = 2021-01-26
 | archive-url = https://web.archive.org/web/20210126003322/https://books.google.com/books?id=NmM-KujxMtoC&pg=PA26
 | url-status = live
}}</ref>]]

While studying electrical conductivity in [[rarefied]] gases in 1859, the German physicist [[Julius Plücker]] observed the radiation emitted from the cathode caused phosphorescent light to appear on the tube wall near the cathode; and the region of the phosphorescent light could be moved by application of a magnetic field.<ref>{{Cite journal|last=Plücker|first=M.|date=1858-12-01|title=XLVI. Observations on the electrical discharge through rarefied gases|url=https://doi.org/10.1080/14786445808642591|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=16|issue=109|pages=408–418|doi=10.1080/14786445808642591|issn=1941-5982}}</ref>  In 1869, Plücker's student [[Johann Wilhelm Hittorf]] found that a solid body placed in between the cathode and the phosphorescence would cast a shadow upon the phosphorescent region of the tube. Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence was caused by the rays striking the tube walls. Furthermore, he also discovered that these rays are deflected by magnets just like lines of current.<ref>{{Cite book |last=Darrigol |first=Olivier |url=https://books.google.com/books?id=ysMf2pAid94C&pg=PA277 |title=Electrodynamics from Ampère to Einstein |date=2003 |publisher=OUP Oxford |isbn=978-0-19-850593-8 |language=en}}</ref>

In 1876, the German physicist [[Eugen Goldstein]] showed that the rays were emitted perpendicular to the cathode surface, which distinguished between the rays that were emitted from the cathode and the incandescent light.  Goldstein dubbed the rays [[cathode ray]]s.<ref name="leicester" /><ref name="Whittaker">
{{cite book
 |last=Whittaker
 |first=E.T.
 |author-link=E. T. Whittaker
 |title=[[A History of the Theories of Aether and Electricity]]
 |volume=1
 |publisher=Nelson |place=London
 |year=1951
}}</ref>{{rp|393}} Decades of experimental and theoretical research involving cathode rays were important in [[J. J. Thomson]]'s eventual discovery of electrons.<ref name="arabatzis" /> Goldstein also experimented with double cathodes and hypothesized that one ray may repulse another, although he didn't believe that any particles might be involved.<ref name=":0">{{Cite journal |last=Thomson |first=George |date=1970 |title=An Unfortunate Experiment: Hertz and the Nature of Cathode Rays |url=https://www.jstor.org/stable/530878 |journal=Notes and Records of the Royal Society of London |volume=25 |issue=2 |pages=237–242 |doi=10.1098/rsnr.1970.0032 |jstor=530878 |issn=0035-9149}}</ref>

During the 1870s, the English chemist and physicist Sir [[William Crookes]] developed the first cathode-ray tube to have a [[vacuum|high vacuum]] inside.<ref name="dekosky">
{{cite journal
 | last = DeKosky | first = R.K.
 | year = 1983
 | title = William Crookes and the quest for absolute vacuum in the 1870s
 | journal = [[Annals of Science]]
 | volume = 40 | issue = 1 | pages = 1–18
 | doi =10.1080/00033798300200101
}}</ref> He then showed in 1874 that the cathode rays can turn a small paddle wheel when placed in their path.  Therefore, he concluded that the rays carried momentum. Furthermore, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged.<ref name="leicester">
{{cite book
 | last = Leicester
 | first = H.M.
 | year = 1971
 | title = The Historical Background of Chemistry
 | url = https://books.google.com/books?id=aJZVQnqcwv4C&pg=PA221
 | pages = 221–222
 | publisher = [[Courier Dover]]
 | isbn = 978-0-486-61053-5
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082418/https://books.google.com/books?id=aJZVQnqcwv4C&pg=PA221
 | url-status = live
}}</ref> In 1879, he proposed that these properties could be explained by regarding cathode rays as composed of negatively charged gaseous [[molecule]]s in a fourth [[state of matter]], in which the mean free path of the particles is so long that collisions may be ignored.<ref name=Whittaker />{{rp|394–395}}

In 1883, not yet well-known German physicist [[Heinrich Hertz]] tried to prove that cathode rays are electrically neutral and got what he interpreted as a confident absence of deflection in electrostatic, as opposed to magnetic, field. However, as [[J. J. Thomson]] explained in 1897, Hertz placed the deflecting electrodes in a highly-conductive area of the tube, resulting in a strong screening effect close to their surface.<ref name=":0" /> 

The German-born British physicist [[Arthur Schuster]] expanded upon Crookes's experiments by placing metal plates parallel to the cathode rays and applying an [[electric potential]] between the plates.<ref name="schu1890">{{Cite journal|last=Schuster|first=Arthur|date=1890|title=The discharge of electricity through gases|journal=Proceedings of the Royal Society of London|volume=47|pages=526–559|doi=10.1098/rspl.1889.0111|s2cid=96197979|doi-access=free}}</ref> The field deflected the rays toward the positively charged plate, providing further evidence that the rays carried negative charge. By measuring the amount of deflection for a given [[electric field|electric]] and [[magnetic field]], in 1890 Schuster was able to estimate the [[Mass-to-charge ratio|charge-to-mass ratio]]{{efn|Older sources list charge-to-mass rather than the modern convention of mass-to-charge ratio.}} of the ray components. However, this produced a value that was more than a thousand times greater than what was expected, so little credence was given to his calculations at the time.<ref name="leicester" /> This is because it was assumed that the charge carriers were much heavier [[hydrogen]] or [[nitrogen]] atoms.<ref name="schu1890" /> Schuster's estimates would subsequently turn out to be largely correct.

In 1892 [[Hendrik Lorentz]] suggested that the mass of these particles (electrons) could be a consequence of their electric charge.<ref>{{cite magazine |first=Frank |last=Wilczek |url=https://www.scientificamerican.com/article.cfm?id=happy-birthday-electron |title=Happy birthday, electron |magazine=Scientific American |date=June 2012 |access-date=2022-02-24 |archive-date=2013-11-01 |archive-url=https://web.archive.org/web/20131101121817/http://www.scientificamerican.com/article.cfm?id=happy-birthday-electron |url-status=live }}</ref>

[[File:J.J Thomson.jpg|thumb|upright|[[J. J. Thomson]]]]
While studying naturally [[Fluorescence|fluorescing]] minerals in 1896, the French physicist [[Henri Becquerel]] discovered that they emitted radiation without any exposure to an external energy source. These [[Radioactive decay|radioactive]] materials became the subject of much interest by scientists, including the New Zealand physicist [[Ernest Rutherford]] who discovered they emitted particles. He designated these particles [[alpha particle|alpha]] and [[beta particle|beta]], on the basis of their ability to penetrate matter.<ref>
{{cite journal
 | last = Trenn | first = T.J.
 | year = 1976
 | title = Rutherford on the Alpha-Beta-Gamma Classification of Radioactive Rays
 | journal = [[Isis (journal)|Isis]]
 | volume = 67 | issue = 1 | pages = 61–75
 | jstor = 231134
 | doi = 10.1086/351545
 | s2cid = 145281124
}}</ref> In 1900, Becquerel showed that the beta rays emitted by [[radium]] could be deflected by an electric field, and that their mass-to-charge ratio was the same as for cathode rays.<ref>
{{cite journal
 | last = Becquerel | first = H.
 | year = 1900
 | title = Déviation du Rayonnement du Radium dans un Champ Électrique
 | journal = [[Comptes rendus de l'Académie des sciences]]
 | volume = 130
 | pages = 809–815
 |language=fr}}
</ref> This evidence strengthened the view that electrons existed as components of atoms.<ref name="BaW9091">[[#refBaW2001|Buchwald and Warwick (2001:90–91).]]</ref><ref>
{{cite journal
 | last = Myers
 | first = W.G.
 | year = 1976
 | title = Becquerel's Discovery of Radioactivity in 1896
 | url = https://jnm.snmjournals.org/cgi/content/abstract/17/7/579
 | journal = [[Journal of Nuclear Medicine]]
 | volume = 17
 | issue = 7
 | pages = 579–582
 | pmid = 775027
 | access-date = 2022-02-24
 | archive-date = 2008-12-22
 | archive-url = https://web.archive.org/web/20081222023947/http://jnm.snmjournals.org/cgi/content/abstract/17/7/579
 | url-status = live
}}</ref>

In 1897, the British physicist [[J. J. Thomson]], with his colleagues [[John Sealy Townsend|John S. Townsend]] and [[Harold A. Wilson (physicist)|H. A. Wilson]], performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier.<ref name="thomson" /> By 1899 he showed that their charge-to-mass ratio, ''e''/''m'', was independent of cathode material.  He further showed that the negatively charged particles produced by radioactive materials, by heated materials and by illuminated materials were universal.<ref name="thomson" /><ref>
{{cite web
 |last         = Thomson
 |first        = J.J.
 |year         = 1906
 |title        = Nobel Lecture: Carriers of Negative Electricity
 |url          = https://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-lecture.pdf
 |publisher    = [[Nobel Foundation|The Nobel Foundation]]
 |access-date  = 2008-08-25 |df=dmy-all
 |archive-url  = https://web.archive.org/web/20081010100408/https://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-lecture.pdf
 |archive-date = 2008-10-10
 |url-status   = dead
}}</ref> Thomson measured ''m''/''e'' for cathode ray "corpuscles", and made good estimates of  the charge ''e'', leading to value for the mass ''m'', finding a value 1400 times less massive than the least massive ion known: hydrogen.<ref name=Whittaker/>{{rp|364}}<ref name="thomson" /> In the same year [[Emil Wiechert]] and [[Walter Kaufmann (physicist)|Walter Kaufmann]] also calculated the ''e''/''m'' ratio but did not take the step of interpreting their results as showing a new particle, while J. J. Thomson would subsequently in 1899 give estimates for the electron charge and mass as well: ''e''&nbsp;≈&nbsp;{{val|6.8|e=-10|u=[[Statcoulomb|esu]]}} and ''m''&nbsp;≈&nbsp;{{val|3|e=-26|u=g}}<ref>{{cite journal|last=[[Abraham Pais]]|date=1997|title=The discovery of the electron – 100 years of elementary particles|url=https://www.slac.stanford.edu/pubs/beamline/pdf/97i.pdf|journal=Beam Line|volume=1|pages=4–16|access-date=2021-09-04|archive-date=2021-09-14|archive-url=https://web.archive.org/web/20210914142755/https://www.slac.stanford.edu/pubs/beamline/pdf/97i.pdf|url-status=live}}</ref><ref>{{cite journal |last=Kaufmann |first=W. |date=1897 |title=Die magnetische Ablenkbarkeit der Kathodenstrahlen und ihre Abhängigkeit vom Entladungspotential |url=https://dx.doi.org/10.1002/andp.18972970709 |journal=Annalen der Physik und Chemie |volume=297 |issue=7 |pages=544–552 |doi=10.1002/andp.18972970709 |bibcode=1897AnP...297..544K |issn=0003-3804 |access-date=2022-02-24 |archive-date=2022-02-24 |archive-url=https://web.archive.org/web/20220224105619/https://onlinelibrary.wiley.com/doi/10.1002/andp.18972970709 |url-status=live }}</ref>
[[File:Millikan.jpg|thumb|upright|[[Robert Andrews Millikan|Robert Millikan]]]]

The name "electron" was adopted for these particles by the scientific community, mainly due to the advocation by [[George Francis FitzGerald|G. F. FitzGerald]], [[Joseph Larmor|J. Larmor]], and [[Hendrik Lorentz|H. A. Lorentz]].<ref name=OHara1975>
{{cite journal
 | last =O'Hara
 | first =J. G.
 | title =George Johnstone Stoney, F.R.S., and the Concept of the Electron
 | journal =Notes and Records of the Royal Society of London
 | volume =29
 | issue =2
 | pages =265–276
 | publisher =Royal Society
 | date =March 1975
 | jstor =531468
 | doi =10.1098/rsnr.1975.0018
 | s2cid =145353314
}}</ref>{{rp|273}} The term was originally coined by [[George Johnstone Stoney]] in 1891 as a tentative name for the basic unit of electrical charge (which had then yet to be discovered).<ref>{{cite journal |last=Stoney |first=George Johnstone |author-link=George Johnstone Stoney |year=1891 |title=On the Cause of Double Lines and of Equidistant Satellites in the Spectra of Gases |journal=The Scientific Transactions of the Royal Dublin Society |volume=4 |pages=583–608 |url=https://digitalarchive.rds.ie/files/show/4769 }}</ref><ref name="GJStoney" />

The electron's charge was more carefully measured by the American physicists [[Robert Andrews Millikan|Robert Millikan]] and [[Harvey Fletcher]] in their [[Oil drop experiment|oil-drop experiment]] of 1909, the results of which were published in 1911. This experiment used an electric field to prevent a charged droplet of oil from falling as a result of gravity. This device could measure the electric charge from as few as 1–150 ions with an error margin of less than 0.3%. Comparable experiments had been done earlier by Thomson's team,<ref name="thomson" /> using clouds of charged water droplets generated by electrolysis, and in 1911 by [[Abram Ioffe]], who independently obtained the same result as Millikan using charged microparticles of metals, then published his results in 1913.<ref>
{{cite journal
 | last1 = Kikoin | first1 = I.K.
 | last2 = Sominskiĭ | first2 = I.S.
 | year = 1961
 | title = Abram Fedorovich Ioffe (on his eightieth birthday)
 | journal = [[Uspekhi Fizicheskikh Nauk|Soviet Physics Uspekhi]]
 | volume = 3 | pages = 798–809
 | doi = 10.1070/PU1961v003n05ABEH005812
 | bibcode = 1961SvPhU...3..798K
 | issue = 5
}} Original publication in Russian: 
{{cite journal
 | last1 = Кикоин | first1 = И.К.
 | last2 = Соминский | first2 = М.С.
 | year = 1960
 | title = Академик А.Ф. Иоффе
 | journal = [[Uspekhi Fizicheskikh Nauk|Успехи Физических Наук]]
 | volume = 72 | issue = 10 | pages = 303–321
 | doi = 10.3367/UFNr.0072.196010e.0307
 | doi-access = free
}}</ref> However, oil drops were more stable than water drops because of their slower evaporation rate, and thus more suited to precise experimentation over longer periods of time.<ref>
{{cite journal
 | last = Millikan
 | first = R.A.
 | year = 1911
 | title = The Isolation of an Ion, a Precision Measurement of its Charge, and the Correction of Stokes's Law
 | journal = [[Physical Review]]
 | volume = 32
 | issue = 2
 | pages = 349–397
 | doi = 10.1103/PhysRevSeriesI.32.349
 | bibcode = 1911PhRvI..32..349M
 | url = https://authors.library.caltech.edu/6437/1/MILpr11b.pdf
 | access-date = 2019-06-21
 | archive-date = 2020-03-17
 | archive-url = https://web.archive.org/web/20200317204458/https://authors.library.caltech.edu/6437/1/MILpr11b.pdf
 | url-status = live
}}</ref>

Around the beginning of the twentieth century, it was found that under certain conditions a fast-moving charged particle caused a condensation of [[supersaturation|supersaturated]] water vapor along its path. In 1911, [[Charles Thomson Rees Wilson|Charles Wilson]] used this principle to devise his [[cloud chamber]] so he could photograph the tracks of charged particles, such as fast-moving electrons.<ref>
{{cite journal
 | last1 = Das Gupta | first1 = N.N.
 | last2 = Ghosh | first2 = S.K.
 | year = 1999
 | title = A Report on the Wilson Cloud Chamber and Its Applications in Physics
 | journal = [[Reviews of Modern Physics]]
 | volume = 18 | pages = 225–290
 | doi = 10.1103/RevModPhys.18.225
 | bibcode=1946RvMP...18..225G
 | issue = 2
}}</ref>

=== Atomic theory ===
[[File:Bohr atom model (mul).svg|right|thumb|alt=Three concentric circles about a nucleus, with an electron moving from the second to the first circle and releasing a photon|The [[Bohr model|Bohr model of the atom]], showing states of an electron with energy [[Quantum number|quantized]] by the number ''n''. An electron dropping to a lower orbit emits a photon equal to the energy difference between the orbits]]
By 1914, experiments by physicists [[Ernest Rutherford]], [[Henry Moseley]], [[James Franck]] and [[Gustav Ludwig Hertz|Gustav Hertz]] had largely established the structure of an atom as a dense [[Atomic nucleus|nucleus]] of positive charge surrounded by lower-mass electrons.<ref name="smirnov" /> In 1913, Danish physicist [[Niels Bohr]] postulated that electrons resided in quantized energy states, with their energies determined by the angular momentum of the electron's orbit about the nucleus. The electrons could move between those states, or orbits, by the emission or absorption of photons of specific frequencies. By means of these quantized orbits, he accurately explained the [[spectral line]]s of the hydrogen atom.<ref>
{{cite web
 | last = Bohr
 | first = N.
 | year = 1922
 | title = Nobel Lecture: The Structure of the Atom
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-12-03
 | df = dmy-all
 | archive-date = 2008-12-03
 | archive-url = https://web.archive.org/web/20081203124237/http://nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-lecture.pdf
 | url-status = live
}}</ref> However, Bohr's model failed to account for the relative intensities of the spectral lines and it was unsuccessful in explaining the spectra of more complex atoms.<ref name="smirnov">
{{cite book
 | last = Smirnov
 | first = B.M.
 | year = 2003
 | title = Physics of Atoms and Ions
 | url = https://books.google.com/books?id=I1O8WYOcUscC&pg=PA14
 | pages = 14–21
 | publisher = [[Springer Science+Business Media|Springer]]
 | isbn = 978-0-387-95550-6
 | access-date = 2020-08-25
 | archive-date = 2020-05-09
 | archive-url = https://web.archive.org/web/20200509044538/https://books.google.com/books?id=I1O8WYOcUscC&pg=PA14
 | url-status = live
}}</ref>

Chemical bonds between atoms were explained by [[Gilbert N. Lewis|Gilbert Newton Lewis]], who in 1916 proposed that a [[covalent bond]] between two atoms is maintained by a pair of electrons shared between them.<ref>
{{cite journal
 | last = Lewis
 | first = G.N.
 | year = 1916
 | title = The Atom and the Molecule
 | journal = [[Journal of the American Chemical Society]]
 | volume = 38
 | issue = 4
 | pages = 762–786
 | doi = 10.1021/ja02261a002
 | bibcode = 1916JAChS..38..762L
 | s2cid = 95865413
 | url = https://zenodo.org/record/1429068
 | access-date = 2019-08-25
 | archive-date = 2019-08-25
 | archive-url = https://web.archive.org/web/20190825132554/https://zenodo.org/record/1429068/files/article.pdf
 | url-status = live
}}</ref> Later, in 1927, [[Walter Heitler]] and [[Fritz London]] gave the full explanation of the electron-pair formation and chemical bonding in terms of [[quantum mechanics]].<ref name=Arabatzis>
{{cite journal
 | last1 = Arabatzis | first1 = T.
 | last2 = Gavroglu | first2 = K.
 | year = 1997
 | title = The chemists' electron
 | journal = [[European Journal of Physics]]
 | volume = 18 | pages = 150–163
 | doi = 10.1088/0143-0807/18/3/005
 | bibcode = 1997EJPh...18..150A
 | issue = 3 | s2cid = 56117976
 | url = https://pdfs.semanticscholar.org/3804/783ac9fc011aeae884a3d370a474cbfdd46f.pdf
 | archive-url = https://web.archive.org/web/20200605041731/https://pdfs.semanticscholar.org/3804/783ac9fc011aeae884a3d370a474cbfdd46f.pdf
 | url-status = dead
 | archive-date = 2020-06-05
}}</ref> In 1919, the American chemist [[Irving Langmuir]] elaborated on the Lewis's static model of the atom and suggested that all electrons were distributed in successive "concentric (nearly) spherical shells, all of equal thickness".<ref>
{{cite journal
 | last = Langmuir
 | first = I.
 | year = 1919
 | title = The Arrangement of Electrons in Atoms and Molecules
 | journal = [[Journal of the American Chemical Society]]
 | volume = 41
 | issue = 6
 | pages = 868–934
 | doi = 10.1021/ja02227a002
 | bibcode = 1919JAChS..41..868L
 | url = https://zenodo.org/record/1429026
 | access-date = 2019-06-21
 | archive-date = 2021-01-26
 | archive-url = https://web.archive.org/web/20210126003324/https://zenodo.org/record/1429026
 | url-status = live
}}</ref> In turn, he divided the shells into a number of cells each of which contained one pair of electrons. With this model Langmuir was able to qualitatively explain the [[chemical property|chemical properties]] of all elements in the periodic table,<ref name=Arabatzis /> which were known to largely repeat themselves according to the [[Periodic table|periodic law]].<ref>
{{cite book
 | last = Scerri | first = E.R.
 | year = 2007
 | title = The Periodic Table
 | url = https://archive.org/details/periodictableits0000scer/page/205
 | url-access = registration | pages=205–226
 | publisher = Oxford University Press
 | isbn = 978-0-19-530573-9
}}</ref>

In 1924, Austrian physicist [[Wolfgang Pauli]] observed that the shell-like structure of the atom could be explained by a set of four parameters that defined every quantum energy state, as long as each state was occupied by no more than a single electron. This prohibition against more than one electron occupying the same quantum energy state became known as the [[Pauli exclusion principle]].<ref>
{{cite book
 | last = Massimi
 | first = M.
 | year = 2005
 | title = Pauli's Exclusion Principle, The Origin and Validation of a Scientific Principle
 | url = https://books.google.com/books?id=YS91Gsbd13cC&pg=PA7
 | pages = 7–8
 | publisher = Cambridge University Press
 | isbn = 978-0-521-83911-2
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204071142/https://books.google.com/books?id=YS91Gsbd13cC&pg=PA7
 | url-status = live
}}</ref> The physical mechanism to explain the fourth parameter, which had two distinct possible values, was provided by the Dutch physicists [[Samuel Goudsmit]] and [[George Uhlenbeck]].  In 1925, they suggested that an electron, in addition to the angular momentum of its orbit, possesses an intrinsic angular momentum and [[magnetic moment|magnetic dipole moment]].<ref name="smirnov" /><ref>
{{cite journal
 | last1 = Uhlenbeck | first1 = G.E.
 | last2 = Goudsmith | first2 = S.
 | year = 1925
 | title = Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons
 | journal = [[Naturwissenschaften|Die Naturwissenschaften]]
 | volume = 13 | issue = 47
 | bibcode = 1925NW.....13..953E
 |doi = 10.1007/BF01558878
 | pages = 953–954 | s2cid = 32211960
 |language=de
}}</ref> This is analogous to the rotation of the Earth on its axis as it orbits the Sun. The intrinsic angular momentum became known as [[Spin (physics)|spin]], and explained the previously mysterious splitting of spectral lines observed with a high-resolution [[Spectrometer|spectrograph]]; this phenomenon is known as [[fine structure]] splitting.<ref>
{{cite journal
 | last = Pauli | first = W.
 | year = 1923
 | title = Über die Gesetzmäßigkeiten des anomalen Zeemaneffektes
 | journal = [[European Physical Journal|Zeitschrift für Physik]]
 | volume = 16 | issue = 1 | pages = 155–164
 | bibcode = 1923ZPhy...16..155P
 | doi = 10.1007/BF01327386
 | s2cid = 122256737
 |language=de
}}</ref>

=== Quantum mechanics ===
{{See also|History of quantum mechanics}}
{{further|#Quantum properties}}
In his 1924 dissertation ''{{lang|fr|Recherches sur la théorie des quanta}}'' (Research on Quantum Theory), French physicist [[Louis de Broglie]] hypothesized that all matter can be represented as a [[Matter wave|de Broglie wave]] in the manner of [[light]].<ref name="de_broglie">
{{cite web
 | last = de Broglie
 | first = L.
 | year = 1929
 | title = Nobel Lecture: The Wave Nature of the Electron
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-08-30
 | df = dmy-all
 | archive-date = 2008-10-04
 | archive-url = https://web.archive.org/web/20081004022001/http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf
 | url-status = live
}}</ref> That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The [[Corpuscular theory of light|corpuscular properties]] of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment.<ref>
{{cite book
 | last = Falkenburg
 | first = B.
 | year = 2007
 | title = Particle Metaphysics: A Critical Account of Subatomic Reality
 | url = https://books.google.com/books?id=EbOz5I9RNrYC&pg=PA85
 | page = 85
 | publisher = [[Springer Science+Business Media|Springer]]
 | isbn = 978-3-540-33731-7
 | bibcode = 2007pmca.book.....F
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082417/https://books.google.com/books?id=EbOz5I9RNrYC&pg=PA85
 | url-status = live
}}</ref> The wave-like nature of light is displayed, for example, when a beam of light is passed through parallel slits thereby creating [[Interference (wave propagation)|interference]] patterns. In 1927, [[George Paget Thomson]] and Alexander Reid discovered the interference effect was produced when a beam of electrons was passed through thin celluloid foils and later metal films, and by American physicists [[Clinton Davisson]] and [[Lester Germer]] by the reflection of electrons from a crystal of [[nickel]].<ref>
{{cite web
 | last = Davisson
 | first = C.
 | year = 1937
 | title = Nobel Lecture: The Discovery of Electron Waves
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-08-30
 | df = dmy-all
 | archive-date = 2008-07-09
 | archive-url = https://web.archive.org/web/20080709090839/http://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf
 | url-status = live
}}</ref> Alexander Reid, who was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident<ref>{{Cite journal |last=Navarro |first=Jaume |date=2010 |title=Electron diffraction chez Thomson: early responses to quantum physics in Britain |url=https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article |journal=The British Journal for the History of Science |language=en |volume=43 |issue=2 |pages=245–275 |doi=10.1017/S0007087410000026 |s2cid=171025814 |issn=0007-0874}}</ref> and is rarely mentioned.

[[File:Orbital s1.png|right|thumb|alt=A spherically symmetric blue cloud that decreases in intensity from the center outward|In quantum mechanics, the behavior of an electron in an atom is described by an [[atomic orbital|orbital]], which is a probability distribution rather than an orbit. In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given [[quantum number]]s, at that point.]]
De Broglie's prediction of a wave nature for electrons led [[Erwin Schrödinger]] to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the [[Schrödinger equation]], successfully described how electron waves propagated.<ref>
{{cite journal
 | last = Schrödinger | first = E.
 | year = 1926
 | title = Quantisierung als Eigenwertproblem
 | journal = [[Annalen der Physik]]
 | volume = 385 | issue = 13 | pages = 437–490
 | bibcode = 1926AnP...385..437S
 | doi = 10.1002/andp.19263851302
 |language=de
}}</ref> Rather than yielding a solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position near where the electron was bound in space, for which the electron wave equations did not change in time. This approach led to a second formulation of [[quantum mechanics]] (the first by Heisenberg in 1925), and solutions of Schrödinger's equation, like Heisenberg's, provided derivations of the energy states of an electron in a hydrogen atom that were equivalent to those that had been derived first by Bohr in 1913, and that were known to reproduce the hydrogen spectrum.<ref>
{{cite book
 | last = Rigden
 | first = J.S.
 | year = 2003
 | title = Hydrogen
 | url = https://books.google.com/books?id=FhFxn_lUvz0C&pg=PT66
 | publisher = Harvard University Press
 | pages = 59–86
 | isbn = 978-0-674-01252-3
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082407/https://books.google.com/books?id=FhFxn_lUvz0C&pg=PT66
 | url-status = live
}}</ref> Once spin and the interaction between multiple electrons were describable, quantum mechanics made it possible to predict the configuration of electrons in atoms with atomic numbers greater than hydrogen.<ref>
{{cite book
 | last = Reed
 | first = B.C.
 | year = 2007
 | title = Quantum Mechanics
 | url = https://books.google.com/books?id=4sluccbpwjsC&pg=PA275
 | pages = 275–350
 | publisher = [[Jones & Bartlett Learning|Jones & Bartlett Publishers]]
 | isbn = 978-0-7637-4451-9
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082419/https://books.google.com/books?id=4sluccbpwjsC&pg=PA275
 | url-status = live
}}</ref>

In 1928, building on Wolfgang Pauli's work, [[Paul Dirac]] produced a model of the electron&nbsp;– the [[Dirac equation]], consistent with [[Principle of relativity|relativity]] theory, by applying relativistic and symmetry considerations to the [[Hamiltonian (quantum mechanics)|hamiltonian]] formulation of the quantum mechanics of the electromagnetic field.<ref>
{{cite journal
 |last         = Dirac
 |first        = P.A.M.
 |year         = 1928
 |title        = The Quantum Theory of the Electron
 |journal      = [[Proceedings of the Royal Society#Proceedings of the Royal Society A|Proceedings of the Royal Society A]]
 |volume       = 117
 |issue        = 778
 |pages        = 610–624
 |doi          = 10.1098/rspa.1928.0023
 |bibcode      = 1928RSPSA.117..610D
 |url          = https://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf
 |doi-access   = free
 |access-date  = 2022-02-24
 |archive-date = 2018-11-25
 |archive-url  = https://web.archive.org/web/20181125224103/http://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf
 |url-status   = live
}}</ref> In order to resolve some problems within his relativistic equation, Dirac developed in 1930 a model of the vacuum as an infinite sea of particles with negative energy, later dubbed the [[Dirac sea]]. This led him to predict the existence of a positron, the [[antimatter]] counterpart of the electron.<ref>
{{cite web
 | last = Dirac
 | first = P.A.M.
 | year = 1933
 | title = Nobel Lecture: Theory of Electrons and Positrons
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-lecture.pdf
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-11-01
 | df = dmy-all
 | archive-date = 2008-07-23
 | archive-url = https://web.archive.org/web/20080723220816/http://nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-lecture.pdf
 | url-status = live
}}</ref> This particle was discovered in 1932 by [[Carl David Anderson|Carl Anderson]], who proposed calling standard electrons ''negatrons'' and using ''electron'' as a generic term to describe both the positively and negatively charged variants.<ref>{{Cite journal |last=Anderson |first=Carl D. |date=1933-03-15 |title=The Positive Electron |journal=Physical Review |language=en |volume=43 |issue=6 |pages=491–494 |doi=10.1103/PhysRev.43.491 |bibcode=1933PhRv...43..491A |issn=0031-899X|doi-access=free }}</ref>

In 1947, [[Willis Lamb]], working in collaboration with graduate student [[Robert Retherford]], found that certain quantum states of the hydrogen atom, which should have the same energy, were shifted in relation to each other; the difference came to be called the [[Lamb shift]]. About the same time, [[Polykarp Kusch]], working with [[Henry M. Foley]], discovered the magnetic moment of the electron is slightly larger than predicted by Dirac's theory. This small difference was later called [[anomalous magnetic dipole moment]] of the electron. This difference was later explained by the theory of [[quantum electrodynamics]], developed by [[Sin-Itiro Tomonaga]], [[Julian Schwinger]] and
[[Richard Feynman]] in the late 1940s.<ref>
{{cite web
 | title = The Nobel Prize in Physics 1965
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1965/
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | access-date = 2008-11-04
 | df = dmy-all
 | archive-date = 2008-10-24
 | archive-url = https://web.archive.org/web/20081024052537/http://nobelprize.org/nobel_prizes/physics/laureates/1965/
 | url-status = live
}}</ref>

=== Particle accelerators ===
With the development of the [[particle accelerator]] during the first half of the twentieth century, physicists began to delve deeper into the properties of [[subatomic particle]]s.<ref>
{{cite journal
 | last = Panofsky
 | first = W.K.H.
 | year = 1997
 | title = The Evolution of Particle Accelerators & Colliders
 | url = https://www.slac.stanford.edu/pubs/beamline/27/1/27-1-panofsky.pdf
 | journal = Beam Line
 | volume = 27
 | issue = 1
 | pages = 36–44
 | access-date = 2008-09-15
 | df = dmy-all
 | archive-date = 2008-09-09
 | archive-url = https://web.archive.org/web/20080909234139/http://www.slac.stanford.edu/pubs/beamline/27/1/27-1-panofsky.pdf
 | url-status = live
}}</ref> The first successful attempt to accelerate electrons using [[electromagnetic induction]] was made in 1942 by [[Donald William Kerst|Donald Kerst]]. His initial [[betatron]] reached energies of 2.3&nbsp;MeV, while subsequent betatrons achieved 300&nbsp;MeV. In 1947, [[synchrotron radiation]] was discovered with a 70&nbsp;MeV electron synchrotron at [[General Electric]]. This radiation was caused by the acceleration of electrons through a magnetic field as they moved near the speed of light.<ref>
{{cite journal
 | last = Elder | first = F.R.
 | year = 1947
 | title = Radiation from Electrons in a Synchrotron
 | journal = [[Physical Review]]
 | volume = 71 | issue = 11 | pages = 829–830
 | doi = 10.1103/PhysRev.71.829.5
 |bibcode = 1947PhRv...71..829E |display-authors=etal
}}</ref>

With a beam energy of 1.5&nbsp;GeV, the first high-energy
particle [[collider]] was [[ADONE]], which began operations in 1968.<ref>
{{cite book
 | last = Hoddeson
 | first = L.
 | year = 1997
 | title = The Rise of the Standard Model: Particle Physics in the 1960s and 1970s
 | url = https://books.google.com/books?id=klLUs2XUmOkC&pg=PA25
 | pages = 25–26
 | publisher = [[Cambridge University Press]]
 | isbn = 978-0-521-57816-5
 | display-authors = etal
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204082414/https://books.google.com/books?id=klLUs2XUmOkC&pg=PA25
 | url-status = live
}}</ref> This device accelerated electrons and positrons in opposite directions, effectively doubling the energy of their collision when compared to striking a static target with an electron.<ref>
{{cite journal
 | last = Bernardini | first = C.
 | year = 2004
 | title = AdA: The First Electron–Positron Collider
 | journal = [[Physics in Perspective]]
 | volume = 6 | issue = 2 | pages = 156–183
 | bibcode = 2004PhP.....6..156B
 | doi = 10.1007/s00016-003-0202-y
 | s2cid = 122534669
}}</ref> The [[Large Electron–Positron Collider]] (LEP) at [[CERN]], which was operational from 1989 to 2000, achieved collision energies of 209&nbsp;GeV and made important measurements for the [[Standard Model]] of particle physics.<ref>
{{cite web
 | year = 2008
 | title = Testing the Standard Model: The LEP experiments
 | url = https://public.web.cern.ch/PUBLIC/en/Research/LEPExp-en.html
 | publisher = [[CERN]]
 | access-date = 2008-09-15
 | df = dmy-all
 | archive-date = 2008-09-14
 | archive-url = https://web.archive.org/web/20080914164129/http://public.web.cern.ch/public/en/Research/LEPExp-en.html
 | url-status = live
}}</ref><ref>
{{cite journal
 | year = 2000
 | title = LEP reaps a final harvest
 | url = https://cerncourier.com/cws/article/cern/28335
 | journal = [[CERN Courier]]
 | volume = 40
 | issue = 10
 | access-date = 2022-02-24
 | archive-date = 2017-09-30
 | archive-url = https://web.archive.org/web/20170930222305/http://cerncourier.com/cws/article/cern/28335
 | url-status = live
}}</ref>

=== Confinement of individual electrons ===
Individual electrons can now be easily confined in ultra small ({{nowrap|1=''L'' = 20 nm}}, {{nowrap|1=''W'' = 20 nm}}) CMOS transistors operated at cryogenic temperature over a range of about 4&nbsp;[[kelvin|K]] (−269&nbsp;°C) to 15&nbsp;[[kelvin|K]] (−258&nbsp;°C).<ref>
{{cite journal
 | last1 = Prati | first1 = E.
 | last2 = De Michielis | first2 = M.
 | last3 = Belli | first3 = M.
 | last4 = Cocco | first4 = S.
 | last5 = Fanciulli | first5 = M.
 | last6 = Kotekar-Patil | first6 = D.
 | last7 = Ruoff | first7 = M.
 | last8 = Kern | first8 = D.P.
 | last9 = Wharam | first9 = D.A.
 | last10 = Verduijn | first10 = J.
 | last11 = Tettamanzi | first11 = G.C.
 | last12 = Rogge | first12 = S.
 | last13 = Roche | first13 = B.
 | last14 = Wacquez | first14 = R.
 | last15 = Jehl | first15 = X.
 | last16 = Vinet | first16 = M.
 | last17 = Sanquer | first17 = M.
 | title = Few electron limit of n-type metal oxide semiconductor single electron transistors
 | journal = Nanotechnology
 | volume = 23 | issue = 21 | pages = 215204
 | year = 2012
 | doi = 10.1088/0957-4484/23/21/215204
 | pmid =  22552118 |arxiv = 1203.4811
 | bibcode = 2012Nanot..23u5204P | citeseerx = 10.1.1.756.4383 | s2cid = 206063658
}}</ref> The electron wavefunction spreads in a semiconductor lattice and negligibly interacts with the valence band electrons, so it can be treated in the single particle formalism, by replacing its mass with the [[effective mass (solid-state physics)|effective-mass tensor]].