Editing Debye length (section)

== In an electrolyte solution ==
In an [[electrolyte]] or a [[colloids|colloidal suspension]], the Debye length<ref name="ISO">International Standard ISO 13099-1, 2012, "Colloidal systems – Methods for Zeta potential determination- Part 1: Electroacoustic and Electrokinetic phenomena"</ref><ref name="Dukhin">{{cite book |last1=Dukhin |first1=A. S. |last2=Goetz |first2=P. J. |title=Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound |publisher=Elsevier |year=2017 |isbn=978-0-444-63908-0 }}</ref><ref>{{cite book |last1=Russel |first1=W. B. |last2=Saville |first2=D. A. |last3=Schowalter |first3=W. R. |title=Colloidal Dispersions |publisher=Cambridge University Press |year=1989 |isbn=0-521-42600-6 }}</ref> for a monovalent electrolyte is usually denoted with symbol {{math|''κ''<sup>−1</sup>}}
<math display="block"> \kappa^{-1} = \sqrt{\frac{\varepsilon_\text{r} \varepsilon_0 k_\text{B} T}{2 e^2 I}}</math>

where
* {{math|''I''}} is the [[ionic strength]] of the electrolyte in number/m<sup>3</sup> units,
* {{math|''ε''<sub>0</sub>}} is the [[Vacuum permittivity|permittivity of free space]],
* {{math|''ε''<sub>r</sub>}} is the [[Relative static permittivity|dielectric constant]],
* {{math|''k''<sub>B</sub>}} is the [[Boltzmann constant]],
* {{math|''T''}} is the absolute temperature in [[kelvin]]s,
* {{math|''e''}} is the [[elementary charge]],

or, for a symmetric monovalent electrolyte,
<math display="block"> \kappa^{-1} = \sqrt{\frac{\varepsilon_\text{r} \varepsilon_0 R T}{2\times10^3 F^2 C_0}}</math>
where
* {{math|''R''}} is the [[gas constant]],
* {{math|''F''}} is the [[Faraday constant]],
* {{math|''C''<sub>0</sub>}} is the electrolyte concentration in [[molar concentration|molar]] units (M or mol/L).

Alternatively,
<math display="block"> \kappa^{-1} = \frac{1}{\sqrt{8\pi \lambda_\text{B} N_\text{A} \times 10^{-24} I}} </math>
where <math>\lambda_\text{B}</math> is the [[Bjerrum length]] of the medium in nm,
and the factor <math> 10^{-24} </math> derives from transforming unit volume from cubic dm to cubic nm.

For deionized water at room temperature, at pH=7, ''λ''<sub>B</sub> ≈ 0.71 nm.

At room temperature ({{convert|20|°C|-1|disp=or}}), one can consider in water the relation:<ref>{{cite book |last=Israelachvili |first=J. |title=Intermolecular and Surface Forces |publisher=Academic Press |year=1985 |isbn=0-12-375181-0 }}</ref>
<math display="block"> \kappa^{-1}(\mathrm{nm}) = \frac{0.304}{\sqrt{I(\mathrm{M})}}</math>
where
* {{math|''κ''<sup>−1</sup>}} is expressed in [[nanometre]]s (nm)
* {{math|''I''}} is the [[ionic strength]] expressed in [[molar concentration|molar]] (M or mol/L)
There is a method of estimating an approximate value of the Debye length in liquids using conductivity, which is described in ISO Standard,<ref name="ISO"/> and the book.<ref name="Dukhin" />