Bjerrum length

The Bjerrum length (named after the Danish chemist Niels Bjerrum ) is the distance at which the electrostatic energy of two charges becomes comparable to the thermal energy .

In the International System of Units (SI) this is given by

${\displaystyle \lambda _{\rm {B}}={\frac {e^{2}}{4\,\pi \,\varepsilon _{0}\,\varepsilon _{\rm {r}}\,k_{\rm {B}}\,T}}}$

and in the cgs system by the formula

${\displaystyle \lambda _{\rm {B}}={\frac {e^{2}}{\varepsilon _{\rm {r}}\,k_{\rm {B}}\,T}}.}$

In water (at 298 K) the Bjerrum length assumes a value of approx. 0.71 nm.