Boltzmann distribution

The Boltzmann distribution is a fundamental principle in physics that describes how particles in a system distribute themselves among different energy levels, particularly when they're in thermal equilibrium. It reveals that particles are more likely to occupy lower energy states than higher ones, but some particles will still have enough thermal energy to reach excited states, creating a predictable statistical pattern. This concept explains everything from why atoms behave as they do in gases to how electrons arrange themselves in molecules, making it essential for understanding chemistry, physics, and even biology at the molecular level.