The Boltzmann distribution is often used to describe the distribution of particles, such as atoms or molecules, over bound states accessible to them. If we have a system consisting of many particles, the probability of a particle being in state is practically the probability that, if we pick a random particle from that system and check what state it is in, we will find it is in state . This probability is equal to the number of particles in state divided by the total number of particles in the system, that is the fraction of particles that occupy state .
The Boltzmann distribution is often used to describe the distribution of particles such as atoms or molecules, over bound states accessible to them. If we have a system consisting of many particles, the probability of a particle being in state is practically the probability that, if we pick a random pa:rticle from that system and check what state it is in, we will find it is in state . This probability is equal to the number of particles in state divided by the total number of particles in the system, that is the fraction of particles that occupy state .