Matter: Hot and Cold

The Boltzmann factor gives the ratio of the numbers of particles in energy states ε joules apart.

e^-ε/kT

Even though it usually represents a tiny proportion, the particles collide many times every second, so the chances of gaining the needed activation energy increases.

This means that the reaction can happen in a matter of seconds.

The Boltzmann factor increases with temperature because the particles have a greater average energy, closer to the activation energy, meaning the reaction will happen faster.

The random thermal energy of a particle is a multiple of the energy kT

As the temperature increases more particles can cross the energy gap characteristic of activation processes

Many processes require particles to have sufficient energy to cross an energy barrier if the process is to occur. For example, molecules in a liquid can escape from the surface to enter the vapour state by breaking apart from other liquid molecules. Particles with sufficient energy can overcome the barrier. Such a process is known as an activation process. 

To escape from a metal surface, a conduction electron must cross an energy barrier: the work function of the surface.

• The number of electrons with energy in excess of the work function Q is approximately proportional to  e^-Q/kT
• If the temperature increases, then e^-Q/kT  increases and more electrons per second are emitted from the surface