The Boltzmann factor is a mathematical expression used in statistical mechanics to describe the probability of a system being in a particular energy state. It is given by the formula e^-E/kT , where E is the energy of the state, k is the Boltzmann constant, and T is the absolute temperature in Kelvin. This factor shows that states with lower energy are more likely to be occupied at higher temperatures. In essence, the Boltzmann factor helps explain how particles distribute themselves among various energy levels in a system. It is fundamental in understanding phenomena in fields like thermodynamics and quantum mechanics, influencing concepts such as thermodynamic equilibrium and entropy.