Home / Topics / Kinetic Theory & Statistical Physics
Maxwell–Boltzmann distribution
Advanced
Distribution of molecular speeds.
f(v) ∝ v²e^{−mv²/2kT}The fraction of molecules with speed v is f(v) ∝ v²e^{−mv²/2kT}: few slow, few very fast, with a peak and a long tail. Higher T broadens and shifts the peak.
The tail explains evaporation and chemical reaction rates.
It describes speeds of a large sample in equilibrium.
In more detail
The Maxwell-Boltzmann distribution gives the fraction of molecules with each speed in a gas at a given temperature. Molecules have a range of speeds, not a single value.
Real-world uses
- Physicists model the speeds of molecules in gases and plasmas.
- Chemists use the distribution to estimate reaction rates.
- Physicists use the Maxwell–Boltzmann distribution to predict the fraction of molecules moving faster than a given speed in a gas.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why does the distribution have a tail?
A few molecules move much faster than average because of random collisions.
How does temperature change it?
Higher temperature widens the distribution and shifts it to higher speeds.
Are all molecules moving at the same speed?
No. They have a wide range of speeds, and the distribution describes how many have each speed at a given temperature.
Related topics in Kinetic Theory & Statistical Physics
Degrees of freedom · Equipartition theorem · Specific heats of gases · Most probable speed · Average, rms and most probable speeds · Law of atmospheres