# Maxwell Boltzmann Distribution Formula

## Maxwell Boltzmann Distribution Formula

The air molecules that surround humans do not move at the same speed. Some air molecules move through the atmosphere more quickly than others, while others move slowly or barely at all. As a result, one inquires about the distribution of speed in gas at a particular temperature rather than the speed of any specific gas molecule. A hypothesis developed by James Maxwell and Ludwig Boltzmann explains how the molecule’s speeds are dispersed in an ideal gas. Students should learn in detail about the Maxwell Boltzmann Distribution Formula. The kinetic theory of gases, which offers a streamlined explanation of many basic gaseous phenomena, such as pressure and diffusion, is what leads to the Maxwell Boltzmann Distribution Formula. The Maxwell Boltzmann Distribution Formula only depends on the speed (or magnitude of velocity) of the particles, yet it applies fundamentally to particle velocities in three dimensions. A particle’s speed will be randomly chosen from the distribution and is more likely to fall inside one range of speeds than another, according to a particle speed probability distribution. The classical ideal gas, which is an idealisation of actual gases, is subject to the kinetic theory of gases.

### Maxwell Boltzmann Distribution Equation

The Maxwell-Boltzmann distribution, often known as the Maxwellian distribution, is a specific probability distribution that bears the names of James Clerk Maxwell and Ludwig Boltzmann in physics (particularly statistical mechanics). It was first used to define and describe the speeds of particles in idealised gases, where the particles travel unhindered inside a stationary container and only collide for extremely brief periods of time to exchange energy and momentum with one another or with their thermal surroundings. In this case, the word “particle” exclusively refers to gaseous particles (atoms or molecules), and it is assumed that the system of particles has attained thermodynamic equilibrium. Maxwell Boltzmann Distribution Formula governs the energies of such particles, and the statistical distribution of speeds is found by equating particle energies with kinetic energy.

### Solved Example

Solved examples on the Maxwell Boltzmann Distribution Formula are provided by Extramarks.