Maxwell-Boltzmann velocity distribution
= Maxwell-Boltzmann velocity distribution
{c}
{title2=$f(\mathbf v)$}
For particles of mass $m$ in a classical gas at temperature $T$, the normalized velocity density is
$$
f(\mathbf v)=
\left(\frac{m}{2\pi k_BT}\right)^{3/2}
\exp\left(-\frac{m|\mathbf v|^2}{2k_BT}\right).
$$
Its Cartesian components are independent centered <normal random variables> of variance $k_BT/m$.