Science collection: Bjerrum length

The Bjerrum length is the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy scale, $k B T$ , where $k B$ is the Boltzmann constant and $T$ is the absolute temperature in Kelvin.

In standard units, the Bjerrum length is given by

$\lambda_B = \frac{e^2}{4\pi \epsilon \ k_B T}$ ,

where $e$ is the elementary charge, $ε$ is the dielectric constant of the medium and $ε 0$ is the vacuum permittivity. For water at room temperature ( $T = 300$ K), $\epsilon \approx 80 \, \epsilon_0$ , so that $\lambda_B \approx 0.7$ nm.