# Thermionic emission and delayed emission

I want to understand the concepts behind the thermionic emission. In thermionic emission, the energy randomization occurs and the energy may be split to electronic or roto-vibrational states. If this energy randomization happens, I didn't understand how the electron will get enough energy to be detached from the molecule/cluster! The randomized energy could be dissipated via radiation (IR or visible). So, to make clear, I am wondering how this randomzed energy can cause electron emission.

As far as I know (from readings), delayed emission of electrons is an indication for thermionic emission (Y Zhao et.al. J. Chem. Phys., 1996, 105(12), 4905). How the electron finally collect these randomized energy so that it eventually get detached?

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Consider the analogy of the velocity distribution in an ideal gas. On average the atoms have an energy of 3/2$kT$, but due to the random nature of atomic collisions some atoms have more energy and some less. The atom velocities end up obeying the Maxwell-Boltzman distribution.
Your reference to "molecule/cluster" suggests you're also considering non-metals, but I'm not sure non-metals show thermionic emission in the sense I understand the term. You can certainly ionise molecules in a non-metal, and again it will be due to local concentrations of energy obeying a Maxwell-Boltzman type distribution. For example, you've probably seen the colours generated by metal ions in fireworks. These are due to electronic excitations even though in the firework $kT$ is well below the energies required. Again it's due to the small fraction of molecules colliding with enough energy to cause an electronic excitation.