Editing Electrical mobility (section)

==Theory==
When a [[charged particle]] in a [[gas]] or [[liquid]] is acted upon by a uniform [[electric field]], it will be accelerated until it reaches a constant [[drift velocity]] according to the formula
<math display="block">v_\text{d} = \mu E,</math>
where 
* <math>v_\text{d}</math> is the drift velocity ([[SI units]]: m/s),
* <math>E</math> is the magnitude of the applied electric field (V/m),
* <math>\mu</math> is the mobility (m<sup>2</sup>/(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:
<math display="block">\mu = \frac{v_\text{d}}{E}.</math>

For example, the mobility of the sodium ion (Na<sup>+</sup>) in water at 25&nbsp;°C is {{val|5.19|e=-8|u=m<sup>2</sup>/(V·s)}}.<ref>[[Keith J. Laidler]] and John H. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), p. 274. {{ISBN|0-8053-5682-7}}.</ref> This means that a sodium ion in an electric field of 1&nbsp;V/m would have an average drift velocity of {{val|5.19|e=-8|u=m/s}}. Such values can be obtained from measurements of [[Molar conductivity#Molar ionic conductivity|ionic conductivity]] in solution.

Electrical mobility is proportional to the net [[electric charge|charge]] of the particle. This was the basis for [[Robert Millikan]]'s demonstration that electrical charges occur in discrete units, whose magnitude is the charge of the [[electron]].

Electrical mobility is also inversely proportional to the [[Stokes radius]] <math>a</math> of the ion, which is the effective radius of the moving ion including any molecules of water or other solvent that move with it. This is true because the solvated ion moving at a constant [[drift velocity]] <math>s</math> is subject to two equal and opposite forces: an electrical force <math>zeE</math> and a frictional force <math>F_\text{drag} = fs = (6 \pi \eta a)s</math>, where <math>f</math> is the frictional coefficient, <math>\eta</math> is the solution viscosity. For different ions with the same charge such as Li<sup>+</sup>, Na<sup>+</sup> and K<sup>+</sup> the electrical forces are equal, so that the drift speed and the mobility are inversely proportional to the radius <math>a</math>.<ref name=Atk>{{cite book |last1=Atkins |first1=P. W. |authorlink1=Peter Atkins |last2=de Paula |first2=J. |date=2006 |title=Physical Chemistry |url=https://archive.org/details/atkinsphysicalch00atki |url-access=limited |edition=8th |isbn=0198700725 |publisher=[[Oxford University Press]] |pages=[https://archive.org/details/atkinsphysicalch00atki/page/n796 764]–6}}</ref> In fact, conductivity measurements show that ionic mobility ''increases'' from Li<sup>+</sup> to Cs<sup>+</sup>, and therefore that Stokes radius ''decreases'' from Li<sup>+</sup> to Cs<sup>+</sup>. This is the opposite of the order of [[Ionic radius|ionic radii]] for crystals and shows that in solution the smaller ions (Li<sup>+</sup>) are more extensively [[solvation shell|hydrated]] than the larger (Cs<sup>+</sup>).<ref name=Atk/>