Editing Elementary charge (section)

=== In terms of the Avogadro constant and Faraday constant ===
If the [[Avogadro constant]] ''N''<sub>A</sub> and the [[Faraday constant]] ''F'' are independently known, the value of the elementary charge can be deduced using the formula
<math display="block">e = \frac{F}{N_\text{A}}.</math>
(In other words, the charge of one [[Mole (unit)|mole]] of electrons, divided by the number of electrons in a mole, equals the charge of a single electron.)

This method is ''not'' how the ''most accurate'' values are measured today. Nevertheless, it is a legitimate and still quite accurate method, and experimental methodologies are described below.

The value of the Avogadro constant ''N''<sub>A</sub> was first approximated by [[Johann Josef Loschmidt]] who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas.<ref>{{cite journal | first = J. | last = Loschmidt | author-link = Johann Josef Loschmidt | title = Zur Grösse der Luftmoleküle | journal = Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien | volume = 52 | issue = 2 | pages = 395–413 | year =1865}} [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation] {{webarchive |url=https://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html |date=February 7, 2006 }}.</ref> Today the value of ''N''<sub>A</sub> can be measured at very high accuracy by taking an extremely pure crystal (often [[silicon]]), measuring how far apart the atoms are spaced using [[X-ray diffraction]] or another method, and accurately measuring the density of the crystal. From this information, one can deduce the mass (''m'') of a single atom; and since the [[molar mass]] (''M'') is known, the number of atoms in a mole can be calculated: {{nowrap|1=''N''<sub>A</sub> = ''M''/''m''}}.

The value of ''F'' can be measured directly using [[Faraday's laws of electrolysis]]. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by [[Michael Faraday]] in 1834.<ref>{{cite journal | author = Ehl, Rosemary Gene |author2=Ihde, Aaron |author-link2=Aaron J. Ihde |title = Faraday's Electrochemical Laws and the Determination of Equivalent Weights | journal = Journal of Chemical Education | year = 1954 | volume = 31 | issue = May | pages = 226–232 | doi = 10.1021/ed031p226 |bibcode = 1954JChEd..31..226E }}</ref> In an [[electrolysis]] experiment, there is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode. Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of [[electric current]]), and also taking into account the molar mass of the ions, one can deduce ''F''.{{physconst|e|ref=only}}

The limit to the precision of the method is the measurement of ''F'': the best experimental value has a relative uncertainty of 1.6&nbsp;ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.<ref>{{cite journal |author-first1=Peter J. |author-last1=Mohr |author-first2=Barry N. |author-last2=Taylor |title=CODATA recommended values of the fundamental physical constants: 1998 |journal=[[Journal of Physical and Chemical Reference Data]] |volume=28 |issue=6 |pages=1713–1852 |bibcode=1999JPCRD..28.1713M |doi=10.1063/1.556049 |year=1999 |url=https://www.nist.gov/pml/div684/fcdc/upload/rmp1998-2.pdf |archive-url=https://web.archive.org/web/20171001122752/https://www.nist.gov/sites/default/files/documents/pml/div684/fcdc/rmp1998-2.pdf|archive-date=2017-10-01}}</ref>