# Electrical mobility > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Electrical_mobility > Markdown URL: https://mediated.wiki/source/Electrical_mobility.md > Source: https://en.wikipedia.org/wiki/Electrical_mobility > Source revision: 1331033466 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Ability of charged particles to move through a medium in response to an electric field For other uses, see [Electric vehicle](/source/Electric_vehicle). For the electrical mobility of an electron or electron hole in solid-state physics, see [Electron mobility](/source/Electron_mobility). **Electrical mobility** is the ability of charged particles (such as [electrons](/source/Electron) or [protons](/source/Proton)) to move through a medium in response to an [electric field](/source/Electric_field) that is pulling them. The separation of ions according to their mobility in gas phase is called [ion mobility spectrometry](/source/Ion_mobility_spectrometry), in liquid phase it is called [electrophoresis](/source/Electrophoresis). ## Theory When a [charged particle](/source/Charged_particle) in a [gas](/source/Gas) or [liquid](/source/Liquid) is acted upon by a uniform [electric field](/source/Electric_field), it will be accelerated until it reaches a constant [drift velocity](/source/Drift_velocity) according to the formula v d = μ E , {\displaystyle v_{\text{d}}=\mu E,} where - v d {\displaystyle v_{\text{d}}} is the drift velocity ([SI units](/source/SI_units): m/s), - E {\displaystyle E} is the magnitude of the applied electric field (V/m), - μ {\displaystyle \mu } is the mobility (m2/(V·s)). In other words, the electrical mobility of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field: μ = v d E . {\displaystyle \mu ={\frac {v_{\text{d}}}{E}}.} For example, the mobility of the sodium ion (Na+) in water at 25 °C is 5.19×10−8 m2/(V·s).[1] This means that a sodium ion in an electric field of 1 V/m would have an average drift velocity of 5.19×10−8 m/s. Such values can be obtained from measurements of [ionic conductivity](/source/Molar_conductivity#Molar_ionic_conductivity) and [transference number](/source/Transference_number) in solution. Electrical mobility is proportional to the net [charge](/source/Electric_charge) of the particle. This was the basis for [Robert Millikan](/source/Robert_Millikan)'s demonstration that electrical charges occur in discrete units, whose magnitude is the charge of the [electron](/source/Electron). Electrical mobility is also inversely proportional to the [Stokes radius](/source/Stokes_radius) a {\displaystyle a} of the ion, which is the effective radius of the moving ion including any molecules of water or other [solvent](/source/Solvent) that move with it. This is true because the solvated ion moving at a constant [drift velocity](/source/Drift_velocity) s {\displaystyle s} is subject to two equal and opposite forces: an electrical force z e E {\displaystyle zeE} and a frictional force F drag = f s = ( 6 π η a ) s {\displaystyle F_{\text{drag}}=fs=(6\pi \eta a)s} , where f {\displaystyle f} is the frictional coefficient, η {\displaystyle \eta } is the solution [viscosity](/source/Viscosity). For different ions with the same charge such as Li+, Na+ and K+ the electrical forces are equal, so that the drift speed and the mobility are inversely proportional to the radius a {\displaystyle a} .[2] In fact, conductivity measurements show that ionic mobility *increases* from Li+ to Cs+, and therefore that Stokes radius *decreases* from Li+ to Cs+. This is the opposite of the order of [ionic radii](/source/Ionic_radius) for crystals and shows that in solution the smaller ions (Li+) are more extensively [hydrated](/source/Solvation_shell) than the larger (Cs+).[2] ## Mobility in gas phase Mobility is defined for any species in the gas phase, encountered mostly in [plasma](/source/Plasma_(physics)) physics and is defined as μ = q m ν m , {\displaystyle \mu ={\frac {q}{m\nu _{\text{m}}}},} where - q {\displaystyle q} is the charge of the species, - ν m {\displaystyle \nu _{\text{m}}} is the momentum-transfer collision frequency, - m {\displaystyle m} is the mass. Mobility is related to the species' **diffusion coefficient** D {\displaystyle D} through an exact (thermodynamically required) equation known as the [Einstein relation](/source/Einstein_relation_(kinetic_theory)): μ = q k T D , {\displaystyle \mu ={\frac {q}{kT}}D,} where - k {\displaystyle k} is the [Boltzmann constant](/source/Boltzmann_constant), - T {\displaystyle T} is the [gas](/source/Gas) temperature, - D {\displaystyle D} is the diffusion coefficient. If one defines the [mean free path](/source/Mean_free_path) in terms of [momentum transfer](/source/Momentum_transfer), then one gets for the diffusion coefficient D = π 8 λ 2 ν m . {\displaystyle D={\frac {\pi }{8}}\lambda ^{2}\nu _{\text{m}}.} But both the *momentum-transfer mean free path* and the *momentum-transfer collision frequency* are difficult to calculate. Many other mean free paths can be defined. In the gas phase, λ {\displaystyle \lambda } is often defined as the diffusional mean free path, by assuming that a simple approximate relation is exact: D = 1 2 λ v , {\displaystyle D={\frac {1}{2}}\lambda v,} where v {\displaystyle v} is the [root mean square](/source/Root_mean_square) speed of the gas molecules: v = 3 k T m , {\displaystyle v={\sqrt {\frac {3kT}{m}}},} where m {\displaystyle m} is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path. ## Applications Electrical mobility is the basis for [electrostatic precipitation](/source/Electrostatic_precipitation), used to remove particles from exhaust gases on an industrial scale. The particles are given a charge by exposing them to ions from an [electrical discharge](/source/Electrical_discharge) in the presence of a strong field. The particles acquire an electrical mobility and are driven by the field to a collecting electrode. Instruments exist which select particles with a narrow range of electrical mobility, or particles with electrical mobility larger than a predefined value.[3] The former are generally referred to as "differential mobility analyzers". The selected mobility is often identified with the diameter of a singly charged spherical particle, thus the "electrical-mobility diameter" becomes a characteristic of the particle, regardless of whether it is actually spherical. Passing particles of the selected mobility to a detector such as a [condensation particle counter](/source/Condensation_particle_counter) allows the number concentration of particles with the currently selected mobility to be measured. By varying the selected mobility over time, mobility vs concentration data may be obtained. This technique is applied in [scanning mobility particle sizers](/source/Scanning_mobility_particle_sizer). ## References 1. **[^](#cite_ref-1)** [Keith J. Laidler](/source/Keith_J._Laidler) and John H. Meiser, *Physical Chemistry* (Benjamin/Cummings 1982), p. 274. [ISBN](/source/ISBN_(identifier)) [0-8053-5682-7](https://en.wikipedia.org/wiki/Special:BookSources/0-8053-5682-7). 1. ^ [***a***](#cite_ref-Atk_2-0) [***b***](#cite_ref-Atk_2-1) [Atkins, P. W.](/source/Peter_Atkins); de Paula, J. (2006). [*Physical Chemistry*](https://archive.org/details/atkinsphysicalch00atki) (8th ed.). [Oxford University Press](/source/Oxford_University_Press). pp. [764](https://archive.org/details/atkinsphysicalch00atki/page/n796)–6. [ISBN](/source/ISBN_(identifier)) [0198700725](https://en.wikipedia.org/wiki/Special:BookSources/0198700725). 1. **[^](#cite_ref-3)** E. O. Knutson and K. T. Whitby (1975). "Aerosol classification by electric mobility: Apparatus, theory, and applications". *J. Aerosol Sci*. **6** (6): 443–451. [Bibcode](/source/Bibcode_(identifier)):[1975JAerS...6..443K](https://ui.adsabs.harvard.edu/abs/1975JAerS...6..443K). [doi](/source/Doi_(identifier)):[10.1016/0021-8502(75)90060-9](https://doi.org/10.1016%2F0021-8502%2875%2990060-9). v t e Electrophoresis History of electrophoresis Techniques Affinity electrophoresis Agarose gel electrophoresis Capillary electrochromatography Capillary electrophoresis Dielectrophoresis Difference gel electrophoresis Discontinuous electrophoresis Electroblotting Electrochromatography Electrophoretic mobility shift assay Gel electrophoresis Immunoelectrophoresis Iontophoresis Isotachophoresis Moving-boundary electrophoresis Polyacrylamide gel electrophoresis Pulsed-field gel electrophoresis Temperature gradient gel electrophoresis Two-dimensional gel electrophoresis Applications DNA laddering DNA separation by silica adsorption Gel electrophoresis of nucleic acids Gel electrophoresis of proteins Serum protein electrophoresis Theory Electrical mobility Isoelectric focusing Journals Electrophoresis (journal) Category Commons Analytical Chemistry Authority control databases GND --- Adapted from the Wikipedia article [Electrical mobility](https://en.wikipedia.org/wiki/Electrical_mobility) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Electrical_mobility?action=history)). 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