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Elementary charge
Description
The elementary charge or proton charge e has the SI unit coulomb [C], but more strictly coulomb per elementary unit [C·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·x^{-1}]. When the charge Q_{el} [C] of a number N_{e} [x] of electrons e is divided by the count N_{e}, then the particle charge Q_{NX} (Q_{NX}) charge per elementary entity is obtained, -e = Q_{el}/N_{e} [C·x^{-1}]. e is also used as an atomic unit.
Abbreviation: e [C·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·x^{-1}], which is charge per count of protons.
Q_{el} ≝ Q_{elp+} [C]
e ≝ Q_{Np+} = Q_{el}·N_{p+}^{-1} [C∙x^{-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" — 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 ρ [C·m^{-3}]. Dividing ρ by the count concentration of electrons [x·m^{-3}], we obtain the unit [C·x^{-1}] for the electron charge. Therefore, electron charge (or proton charge) is clearly the charge per particle.
Ambiguity of Q_{B}
- IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as
IUPAC: z_{B} = Q_{B}·e^{-1}
- Therefore, Q_{B} = z_{B}∙e. The subscript in Q_{B} indicates per elementary entity B. This is opposite to the subscript in V_{B} as the symbol for the volume of a substance of type B (e.g. V_{O2} [L]). For consistency with this convention, the symbol Q_{elB} or Q_{elX} [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 Q_{NX} [C∙x^{-1}]. To avoid too long and multiple subscript levels, Q_{NX} is used instead of Q_{UX}, and the ‘el’ is dropped from Q_{elNX}. The particle charge Q_{NH+} per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is z_{H+} = Q_{NH+}/e = 1. In summary:
z_{B} = Q_{NB}·e^{-1}
Q_{NB} = Q_{elB}·N_{B}^{-1} [C∙x^{-1}]
Keywords
- » charge Q_{elX}
- » charge number z_{X}
- » electrochemical constant f
- » elementary charge e
- » Faraday constant F
- » hydrogen ion versus proton
- » iconic symbols
- » motive entity
- » particle charge Q_{NX}
- Bioblast links: Charge - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
- 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 Q_{elX}, N_{X}, n_{X}, V_{X}, m_{X}, 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 Q_{elX} [C] / count N_{X} [x] = Q_{NX} [C·x^{-1}] particle charge (IUPAC: Q_{B}) charge Q_{elX} [C] / amount n_{X} [mol] = Q_{nX} [C·mol^{-1}] charge number times Faraday constant charge Q_{elX} [C] / volume V_{X} [m^{3}] = Q_{VX} [C·m^{-3}] ρ_{el} charge density charge Q_{elX} [C] / mass m_{X} [kg] = Q_{mX} [C·kg^{-1}] specific charge count N_{X} [x] / charge Q_{elX} [C] = N_{eX} [x·C^{-1}] amount n_{X} [mol] / charge Q_{elX} [C] = n_{eX} [mol·C^{-1}] volume V_{X} [m^{3}] / charge Q_{elX} [C] = V_{eX} [m^{3}·C^{-1}] ρ_{el}^{-1} mass m_{X} [kg] / charge Q_{elX} [C] = m_{eX} [kg·C^{-1}]
- Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
- Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment elementary U_{X} elementary unit [x] U_{X}, U_{B}; [x] not in SI count N_{X} elementary unit [x] N_{X}, N_{B}; [x] not in SI number N - dimensionless = N_{X}·U_{X}^{-1} amount of substance n_{B} mole [mol] n_{X}, n_{B} electric current I ampere [A] A = C·s^{-1} time t second [s] length l meter [m] SI: metre mass m kilogram [kg] thermodynamic temperature T kelvin [K] luminous intensity I_{V} candela [cd]
- Fundamental relationships
- » Avogadro constant N_{A}
- » Boltzmann constant k
- » elementary charge e
- » Faraday constant F
- » gas constant R
- » electrochemical constant f
- Fundamental relationships
- SI and related concepts
References
- Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - »Bioblast link«
- Cohen ER, Cvitas T, Frey JG, Holmström 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. - »Bioblast link«
- Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2 - »Bioblast link«
- 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.
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