Elementary charge

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Elementary charge


Table Physical constants.png

The elementary charge or proton charge e has the SI unit coulomb [C], but more strictly coulomb per elementary unit [C路x-1]. -e is the charge per electron. Elementary charge e is the charge per elementary entity H+ with SI unit [C] but canonical SI unit [C路x-1]. When the charge Qel [C] of a number Ne [x] of electrons e is divided by the count Ne, then the particle charge QNX (QNX) charge per elementary entity is obtained, -e = Qel/Ne [C路x-1]. e is also used as an atomic unit.

Abbreviation: e [C路x-1]

Reference: Bureau International des Poids et Mesures 2019 The International System of Units (SI), Gibney 2017 Nature

Communicated by Gnaiger E (2018-10-18) last update 2020-12-01

Canonical comments on IUPAC definitions in the context of charge

Charge of the proton versus charge per proton

Proton charge is the elementary charge e [C路x-1], which is charge per count of protons.
QelQelp+ [C]
eQNp+ = QelNp+-1  [C鈭檟-1]
The distinction of charge of particles versus charge per single particle is not made sufficiently clear by IUPAC, when defining "-e is the charge of an electron" 鈥 it must be corrected to "-e is the charge per electron".
For comparison, the name "charge density of electrons" is used by IUPAC with symbol [C路m-3]. Dividing by the count concentration of electrons [x路m-3], we obtain the unit [C路x-1] for the electron charge. Therefore, electron charge (or proton charge) is clearly the charge per particle.

Ambiguity of QB

IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as
IUPAC:  zB = QBe-1
Therefore, QB = zBe. The subscript in QB indicates per elementary entity B. This is opposite to the subscript in VB as the symbol for the volume of a substance of type B (e.g. VO2 [L]). For consistency with this convention, the symbol QelB or QelX [C] is used for indicating charge of a substance of type B or X, distinguished from particle charge as the quantity of charge per elementary entity X with symbol QNX [C鈭檟-1]. To avoid too long and multiple subscript levels, QNX is used instead of QUX, and the 鈥榚l鈥 is dropped from QelNX. The particle charge QNH+ per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is zH+ = QNH+/e = 1. In summary:
zB = QNBe-1
QNB = QelBNB-1 [C鈭檟-1]


charge QelX
charge number zX
electrochemical constant f
elementary charge e
Faraday constant F
hydrogen ion versus proton
iconic symbols
motive entity
particle charge QNX


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Table Physical constants.png

Normalization of charge and iconic symbols
Iconic symbols show the quantity, the format of the normalization in the subscript (N, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities QelX, NX, nX, VX, mX, the subscript X without attachment to a format indicates the quantity of X.
Quantity Unit Normalized for quantity Unit Iconic symbol Unit Practical symbol Quantity
charge QelX [C] / count NX [x] = QNX [C路x-1] particle charge (IUPAC: QB)
charge QelX [C] / amount nX [mol] = QnX [C路mol-1] charge number times Faraday constant
charge QelX [C] / volume VX [m3] = QVX [C路m-3] el charge density
charge QelX [C] / mass mX [kg] = QmX [C路kg-1] specific charge
count NX [x] / charge QelX [C] = NeX [x路C-1]
amount nX [mol] / charge QelX [C] = neX [mol路C-1]
volume VX [m3] / charge QelX [C] = VeX [m3路C-1] el-1
mass mX [kg] / charge QelX [C] = meX [kg路C-1]


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Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment
elementary UX elementary unit [x] UX, UB; [x] not in SI
count NX elementary unit [x] NX, NB; [x] not in SI
number N - dimensionless = NXUX-1
amount of substance nB mole [mol] nX, nB
electric current I ampere [A] A = C路s-1
time t second [s]
length l meter [m] SI: metre
mass m kilogram [kg]
thermodynamic temperature T kelvin [K]
luminous intensity IV candela [cd]
Fundamental relationships
Avogadro constant NA
Boltzmann constant k
elementary charge e
Faraday constant F
gas constant R
electrochemical constant f
SI and related concepts
International System of Units
elementary unit x
SI prefixes
International Union of Pure and Applied Chemistry, IUPAC
motive unit
iconic symbols


  1. Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - 禄Bioblast link芦
  2. Cohen ER, Cvitas T, Frey JG, Holmstr枚m B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry. IUPAC Green Book 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge. - 禄Bioblast link芦
  3. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2 - 禄Bioblast link芦
  4. Gnaiger Erich (2020) Canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprint Arch 2020.4 doi:10.26124/mitofit:200004.

MitoPedia concepts: Ergodynamics 

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