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{|  class="wikitable" style="float: right;"
! Values of ''m''<sub>e</sub>
! Units
|-
| 9.10938215(45){{e|&minus;31}} || [[kilogram|kg]]
|-
| 5.4857990943(23){{e|&minus;4}} || [[atomic mass unit|u]]
|-
| 8.18710438(41){{e|&minus;14}}  || [[Joule|J/c<sup>2</sup>]]
|-
| 0.510998910(13) || [[Electronvolt|MeV/c<sup>2</sup>]]
|-
! Values of the energy of ''m''<sub>e</sub>
! Units
|-
| 8.18710438(41){{e|&minus;14}}  || [[Joule|J]]
|-
| 0.510998910(13) || [[Electronvolt|MeV]]
|-
|}


The '''electron rest mass''' (symbol: ''m''<sub>e</sub>) is the [[Mass in special relativity|mass]] of a stationary [[electron]]. It is one of the fundamental [[Physical constant|constants]] of [[physics]], and is also very important in [[chemistry]] because of its relation to the [[Avogadro constant]]. It has a value of about 9.11{{e|&minus;31}} [[kilogram]]s or about 5.486{{e|&minus;4}} [[atomic mass unit]]s, [[Mass–energy equivalence|equivalent]] to an [[energy]] of about 8.19{{e|&minus;14}} [[joule]]s or about 0.511 [[Electronvolt|megaelectronvolts]].<ref name="CODATA">{{CODATA2006}}</ref>


== Terminology ==
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The term "rest mass" + kinetic energy comes from the need to take account of the effects of [[special relativity]] on the apparent (or "observed") mass of an electron. It is impossible to "weigh" a stationary electron, and so all practical measurements must be carried out on moving electrons. However special relativity shows that the mass of an object appears to increase as its speed ''v'' (relative to the rest frame) increases.
 
== Determination ==
The electron rest mass in kilograms is calculated from the definition of the [[Rydberg constant]] ''R''<sub>∞</sub>:
 
:<math>R_{\infty} = \frac{m_{\rm e}c\alpha^2}{2h} \Rightarrow m_{\rm e} = \frac{2R_{\infty}h}{c\alpha^2}</math>
 
where ''α'' is the [[fine structure constant]] and ''h'' is the [[Planck constant]].<ref name="CODATA" />  The relative uncertainty, 5{{e|&minus;8}} in the 2006 CODATA recommended value,<ref name="NIST">{{citation | title = The NIST reference on Constants, Units, and Uncertainty | url = http://physics.nist.gov/cuu/index.html | publisher = [[National Institute of Standards and Technology]]}}</ref> is due entirely to the uncertainty in the value of the Planck constant.
 
The electron relative atomic mass can be measured directly in a [[Penning trap]]. It can also be inferred from the spectra of [[antiprotonic helium]] atoms ([[helium]] atoms where one of the electrons has been replaced by an [[antiproton]]) or from measurements of the electron [[G-factor|''g''-factor]] in the hydrogenic ions <sup>12</sup>C<sup>5+</sup> or <sup>16</sup>O<sup>7+</sup>. The 2006 CODATA recommended value has a relative uncertainty of 4.2{{e|&minus;10}}.<ref name="CODATA" />
 
The electron relative atomic mass is an adjusted parameter in the CODATA set of fundamental physical constants, while the electron rest mass in kilograms is calculated from the values of the Planck constant, the fine structure constant and the Rydberg constant.<ref name="CODATA" /> The correlation between the two values is negligible (''r''&nbsp;= 0.0003).<ref name="NIST" />
 
== Relationship to other physical constants ==
As mentioned above, the electron mass is used to calculate the [[Avogadro constant]] ''N''<sub>A</sub>:
:<math>N_{\rm A} = \frac{M_{\rm u} A_{\rm r}({\rm e})}{m_{\rm e}} = \frac{M_{\rm u} A_{\rm r}({\rm e})c\alpha^2}{2R_\infty h}</math>
Hence it is also related to the [[atomic mass constant]] ''m''<sub>u</sub>:
:<math>m_{\rm u} = \frac{N_{\rm A}}{M_{\rm u}} = \frac{A_{\rm r}({\rm e})}{m_{\rm e}} = \frac{A_{\rm r}({\rm e})c\alpha^2}{2R_\infty h}</math>
Note that ''m''<sub>u</sub> is defined in terms of ''A''<sub>r</sub>(e), and not the other way round, and so the name "electron mass in atomic mass units" for ''A''<sub>r</sub>(e) involves a circular definition (at least in terms of practical measurements).
 
The electron relative atomic mass also enters into the calculation of all other relative atomic masses. By convention, relative atomic masses are quoted for neutral atoms, but the actual measurements are made on positive [[ion]]s, either in a [[mass spectrometer]] or a [[Penning trap]]. Hence the mass of the electrons must be added back on to the measured values before tabulation. A correction must also be made for the mass equivalent of the [[binding energy]] ''E''<sub>b</sub>. Taking the simplest case of complete ionization of all electrons, for a nuclide X of [[atomic number]] ''Z'',<ref name="CODATA" />
:<math>A_{\rm r}({\rm X}) = A_{\rm r}({\rm X}^{Z+}) + ZA_{\rm r}({\rm e}) - E_{\rm b}/m_{\rm u}c^2\,</math>
As relative atomic masses are measured as ratios of masses, the corrections must be applied to both ions: fortunately, the uncertainties in the corrections are negligible, as illustrated below for hydrogen 1 and oxygen 16.
 
{| class="wikitable"
|-
! &nbsp;
! <sup>1</sup>H
! <sup>16</sup>O
|-
| relative atomic mass of the X<sup>''Z''+</sup> ion
| 1.007&thinsp;276&thinsp;466&thinsp;77(10)
| 15.990&thinsp;528&thinsp;174&thinsp;45(18)
|-
| relative atomic mass of the ''Z'' electrons
| 0.000&thinsp;548&thinsp;579&thinsp;909&thinsp;43(23)
| 0.004&thinsp;388&thinsp;639&thinsp;2754(18)
|-
| correction for the binding energy
| &minus;0.000&thinsp;000&thinsp;014&thinsp;5985
| &minus;0.000&thinsp;002&thinsp;194&thinsp;1559
|-
| '''relative atomic mass of the neutral atom'''
| 1.007&thinsp;825&thinsp;032&thinsp;07(10)
| 15.994&thinsp;914&thinsp;619&thinsp;57(18)
|-
|}
 
The principle can be shown by the determination of the electron relative atomic mass by Farnham ''et al.'' at the University of Washington (1995).<ref>{{citation | doi = 10.1103/PhysRevLett.75.3598 | last1 = Farnham | first1 = D. L. | last2 = Van Dyck, Jr. | first2 = R. S. | last3 = Schwinberg | first3 = P. B. | title = Determination of the Electron's Atomic Mass and the Proton/Electron Mass Ratio via Penning Trap Mass Spectroscopy | journal = [[Physical Review Letters|Phys. Rev. Lett.]] | year = 1995 | volume = 75 | issue = 20 | pages = 3598–3601 | bibcode=1995PhRvL..75.3598F}}</ref> It involves the measurement of the frequencies of the [[cyclotron radiation]] emitted by electrons and by <sup>12</sup>C<sup>6+</sup> ions in a Penning trap. The ratio of the two frequencies is equal to six times the inverse ratio of the masses of the two particles (the heavier the particle, the lower the frequency of the cyclotron radiation; the higher the charge on the particle, the higher the frequency):
:<math>\frac{\nu_c ({}^{12}{\rm C}^{6+})}{\nu_c ({\rm e})} = \frac{6A_{\rm r}({\rm e})}{A_{\rm r}({}^{12}{\rm C}^{6+})} = 0.000\,274\,365\,185\,89(58)</math>
As the relative atomic mass of <sup>12</sup>C<sup>6+</sup> ions is very nearly 12, the ratio of frequencies can be used to calculate a first approximation to ''A''<sub>r</sub>(e), {{nowrap|5.486&thinsp;303&thinsp;7178{{e|&minus;4}}}}. This approximate value is then used to calculate a first approximation to ''A''<sub>r</sub>(<sup>12</sup>C<sup>6+</sup>), knowing that ''E''<sub>b</sub>(<sup>12</sup>C)/''m''<sub>u</sub>''c''<sup>2</sup> (from the sum of the six ionization energies of carbon) is {{nowrap|1.105&thinsp;8674{{e|&minus;6}}}}: ''A''<sub>r</sub>(<sup>12</sup>C<sup>6+</sup>)&nbsp;≈ {{nowrap|11.996&thinsp;708&thinsp;723&thinsp;6367}}. This value is then used to calculate a new approximation to ''A''<sub>r</sub>(e), and the process repeated until the values no longer vary (given the relative uncertainty of the measurement, 2.1{{e|&minus;9}}): this happens by the fourth cycle of iterations for these results, giving ''A''<sub>r</sub>(e)&nbsp;= {{nowrap|5.485&thinsp;799&thinsp;111(12){{e|&minus;4}}}} for these data.
 
== References ==
{{reflist}}
 
[[Category:Electron]]
[[Category:Mass]]
[[Category:Physical constants]]

Latest revision as of 10:54, 20 October 2014


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