# Maxwell–Boltzmann distribution (Probability density function)

## Description

In physics, particularly statistical mechanics, the Maxwell–Boltzmann distribution or Maxwell speed distribution describes particle speeds in idealized gases where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. Particle in this context refers to gaseous atoms or molecules, and the system of particles is assumed to have reached thermodynamic equilibrium. The distribution is a probability distribution for the speed of a particle within the gas – the magnitude of its velocity. This probability distribution indicates which speeds are more likely: a particle will have a speed selected randomly from the distribution, and is more likely to be within one range of speeds than another. The distribution depends on the temperature of the system and the mass of the particle.

This probability density function gives the probability, per unit speed, of finding the particle with a speed near v.

## Variables

f_{v} | Probability density function (s/m) |

m | The particle mass (in MeV/c^2 =1.7826618e-30 kg) (kg) |

π | pi |

k | Boltzmann constant |

T | The absolute temperature (K) |

v | The particle speed (m/s) |

e | e |