Editing Electron (section)

=== Motion and energy ===
According to [[Albert Einstein|Einstein's]] theory of [[special relativity]], as an electron's speed approaches the [[speed of light]], from an observer's point of view its [[Mass in special relativity|relativistic mass]] increases, thereby making it more and more difficult to accelerate it from within the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in vacuum, ''c''. However, when relativistic electrons—that is, electrons moving at a speed close to ''c''—are injected into a dielectric medium such as water, where the local speed of light is significantly less than ''c'', the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called [[Cherenkov radiation]].<ref>{{cite web
 | title = The Nobel Prize in Physics 1958, for the discovery and the interpretation of the Cherenkov effect
 | publisher = [[Nobel Foundation|The Nobel Foundation]]
 | year = 2008
 | url = https://nobelprize.org/nobel_prizes/physics/laureates/1958/
 | access-date = 2008-09-25
 | df = dmy-all
 | archive-date = 2008-10-18
 | archive-url = https://web.archive.org/web/20081018162638/http://nobelprize.org/nobel_prizes/physics/laureates/1958/
 | url-status = live
 }}</ref>

[[File:Lorentz factor.svg|thumb|right|alt=The plot starts at zero and curves sharply upward toward the right|Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as ''v'' approaches ''c''.]]
The effects of special relativity are based on a quantity known as the [[Lorentz factor]], defined as <math>\scriptstyle\gamma=1/ \sqrt{ 1-{v^2}/{c^2} }</math> where ''v'' is the speed of the particle. The kinetic energy ''K''<sub>e</sub> of an electron moving with velocity ''v'' is:
:<math>\displaystyle K_{\mathrm{e}} = (\gamma - 1)m_{\mathrm{e}} c^2,</math>
where ''m''<sub>e</sub> is the mass of electron. For example, the [[SLAC National Accelerator Laboratory|Stanford linear accelerator]] can [[Acceleration|accelerate]] an electron to roughly 51&nbsp;GeV.<ref>{{cite web
 | date = August 26, 2008
 | title = Special Relativity
 | publisher = [[SLAC National Accelerator Laboratory|Stanford Linear Accelerator Center]]
 | url = https://www2.slac.stanford.edu/vvc/theory/relativity.html
 | access-date = 2008-09-25
 | df = dmy-all
 | archive-date = 2008-08-28
 | archive-url = https://web.archive.org/web/20080828113927/http://www2.slac.stanford.edu/VVC/theory/relativity.html
 | url-status = live
 }}</ref>
Since an electron behaves as a wave, at a given velocity it has a characteristic [[Matter wave|de Broglie wavelength]]. This is given by ''λ''<sub>e</sub>&nbsp;=&nbsp;''h''/''p'' where ''h'' is the [[Planck constant]] and ''p'' is the momentum.<ref name="de_broglie" /> For the 51&nbsp;GeV electron above, the wavelength is about {{val|2.4|e=-17|u=m}}, small enough to explore structures well below the size of an atomic nucleus.<ref>{{cite book
 | last = Adams
 | first = S.
 | title = Frontiers: Twentieth Century Physics
 | url = https://books.google.com/books?id=yIsMaQblCisC&pg=PA215
 | page = 215
 | publisher = [[CRC Press]]
 | year = 2000
 | isbn = 978-0-7484-0840-5
 | access-date = 2020-08-25
 | archive-date = 2022-02-04
 | archive-url = https://web.archive.org/web/20220204071142/https://books.google.com/books?id=yIsMaQblCisC&pg=PA215
 | url-status = live
 }}</ref>