By Andrew Phillips
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Extra resources for Ado’s theorem
Here’s the twist though; quantum mechanics itself doesn’t actually lay down totally strict rules; it says that under certain conditions in the subatomic world, some things are much more likely to happen than others so in laying down the selection rules for electron transitions within atoms, it’s really just saying that some bound–bound transitions are very likely to happen whereas others are very unlikely to happen. This is a set of rules which is basically asking to be broken and out there in the real Universe they do indeed get broken.
The incoming energy may be in the form of a photon of sufficient energy to free an electron and this process is often referred to as photoionisation. As with excitation, it’s also possible to ionise the atoms of a gas by sufficient heating and this process is called thermal ionisation. As with thermal excitation, thermal ionisation, as we shall see is of fundamental importance in the formation of stellar spectra. The simplest of all atoms, hydrogen (H) has just one electron, so in this case ionisation can happen just once leaving a hydrogen ion.
The selection rules for electron transitions between energy levels are as follows: r The l quantum number must change by +1 or by −1. r The spin quantum number s does not change. The second rule says that an electron which starts off as spin up will remain a spin up electron after the transition. It means for example that if our electron is spin up and a possible transition would take it to a level whose l number differs by 1 (so the first rule is obeyed) but that level already contains a spin up electron, then it can’t go there.