Editing Debye length (section)

{{Short description|Measure of electrostatic effect and how far it persists}}

In [[plasma (physics)|plasmas]] and [[electrolyte]]s, the '''Debye length''' '''<math>\lambda_\text{D}</math>''' ('''Debye radius''' or '''Debye–Hückel screening length'''), is a measure of a [[charge carrier]]'s net electrostatic effect in a [[Solution (chemistry)|solution]] and how far its electrostatic effect persists.<ref>{{cite journal |url=http://digital.library.wisc.edu/1793/79225 |last1=Debye |first1=P. |last2=Hückel |first2=E. |orig-year=1923 |trans-title=The theory of electrolytes. I. Freezing point depression and related phenomenon |title=Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen |journal=[[Physikalische Zeitschrift]] |volume=24 |issue=9 |pages=185–206 |translator-first=Michael J. |translator-last=Braus |year=2019 }}</ref>  With each Debye length the charges are increasingly [[Electric-field screening|electrically screened]] and the electric potential decreases in magnitude by [[E (mathematical constant)|e]]. A '''Debye sphere''' is a volume whose radius is the Debye length. Debye length is an important parameter in [[plasma physics]], [[electrolytes]], and [[colloids]] ([[DLVO theory]]).

The Debye length for a plasma consisting of particles with density <math>n</math>, charge <math>q</math>, and temperature <math>T</math> is given by <math> \lambda_\text{D}^2 = \varepsilon_0 k_\text{B}T/(n q^2) </math>. The corresponding Debye screening [[wavenumber]] is given by <math> 1/\lambda_\text{D} </math>. The analogous quantities at very low temperatures (<math>T \to 0</math>) are known as the [[Thomas–Fermi screening|Thomas–Fermi length]] and the Thomas–Fermi wavenumber, respectively. They are of interest in describing the behaviour of electrons in metals at room temperature and [[warm dense matter]].

The Debye length is named after the Dutch-American physicist and chemist [[Peter Debye]] (1884–1966), a Nobel laureate in Chemistry.