 So, the idea of fluorescence is subtly different from the idea of phosphorescence, which is a different type of luminescence phenomenon. Phosphorescence is what happens, for example, in a consumer product, you're familiar with that if you have something that glows in the dark, maybe it'll glow in the dark t-shirt or glow in the dark sticker or something like that, something that you have to expose to the light and charge it up and then it will glow for a while if you're in a dark room. We know that's not the same as fluorescence because a fluorescent object, as soon as you turn off the light source, as soon as you turn off, for example, the ultraviolet light that's causing your socks to glow white under a black light, as soon as you turn that off, the fluorescence stops. Phosphorescence is different because you charge it up and it holds onto that energy and lets the emission take place over a longer period of time. So it turns out we can also understand what's going on in phosphorescence with a combination of the Frank-Condon effect and the idea of the electronic selection rules for electronic transitions. So if we have an electronic state with a bunch of different vibrational levels within that energy well, some other excited electronic states, and here I've drawn both an s equals zero singlet state, an excited electronic singlet state, but also an excited electronic triplet state, one with spin one. So the selection rules tell us that when we excite a molecule from this ground electronic state, it has to go to the electronic state with the same spin, not to the one with the different spin. So if we consider what happens when we take a molecule on the ground state and excite it, that vibrational, that vertical transition, Frank-Condon transition, the vertical transition will result in a vibrational excited state in this upper electronic manifold. So perhaps to the state right here, it will not land in the triplet state because that violates the selection rules. So if we excite the molecule, we know from talking about fluorescence that the next thing that's going to happen is vibrational relaxation because that step is very fast. We'll give you some time scales, vibrational relaxation. That happens on the time scale of an individual bond vibration. The frequency of a bond vibration is such that the period of that motion is in the tens of femtoseconds. So roughly every few tens of femtoseconds, this molecule will fall down to a lower vibrational state. So that happens on a time scale of something like 10 to the minus 14th seconds, roughly speaking. So very, very quickly. If this were to continue all the way down to the bottom of the well and the molecule falls from the ground vibrational state of the excited electronic state down to some vibrationally excited state down below, that would be the process we've talked about already as fluorescence. I'll put that in parentheses down here because that's not the main thing we're talking about right now. That process, the fluorescence process, that happens on time scales of nanoseconds or so. So vibrational relaxation much faster, many orders of magnitude faster than fluorescence. Several bond vibrational lifetimes later, the molecule sitting in the ground vibrational state, it then sits around for maybe 10,000 vibrations of the molecule until it decides to electronically relax and then do more vibrational relaxation. That would be the fluorescence process. However, if there's a nearby single state, a spin forbidden state that it couldn't be excited into, it just may happen that some of these vibrational excited states in the triplet electronic state may happen to line up pretty well with the vibrational excited states in the singlet well that we've excited the molecule into. And if that's the case, so for this molecule, let's say this energy level and this energy level line up in energy pretty well, then instead of vibrational relaxing from this singlet vibrational excited state further down, it may undergo what's called intersystem crossing. So let's label these. One was excitation, two was vibrational relaxation. Instead of vibrational relaxing all the way down to the ground vibrational state, it may hop over onto the singlet manifold. So that step is called intersystem crossing. And that's a key step in this phosphorescence process. That can be fast or can be slow. It depends largely on the overlap between these energy levels. If there's a good overlap between them or not, it can happen very quickly. It can happen on the peak a second time scale or it can happen quite slowly if there's not as good an overlap. So entirely depends on the molecules we're talking about how likely that intersystem crossing is. But it's generally more rare than fluorescence. And it's also crucial to notice that that is a non-radiative process, meaning it does not involve electromagnetic radiation, it doesn't involve light. You might have already been saying, how can I get from the singlet state to the triplet state? That's supposed to be forbidden. And it is forbidden to make that spin zero to spin one transition if we're making the transition involved with using light. We can't make the molecule absorb light or emit light in order to change from the singlet state to the triplet state. But the molecule can decide through other means, through collisions, for example, to exchange energy with another molecule through a collision. That is a non-radiative process that doesn't involve light so it doesn't need to obey those same selection rules. So that process that doesn't involve electromagnetic radiation can occur getting you from the singlet onto the triplet state. And then once you're in this blue triplet electronic surface, the molecule can then vibrationally relax in the triplet surface, landing itself at this ground vibrational state in the electronically excited triplet state. That's if I call those steps after the intersystem crossing more vibrational relaxation. So vibrational relaxation happens in step four. We very rapidly after a few bond vibrations ended up in the ground vibrational state up here. And now what does the molecule do? It looks like it's stuck. There's no way to decrease its energy other than going down to this singlet electronic state but it can't get there by emitting light because that would violate the selection rules. What it does is it hangs out there up in the ground vibrational state of this triplet electronic state because it can't do anything else except for the fact that those selection rules, just like they were for the harmonic oscillator and rigid rotor, they're not perfect. The forbidden transitions are not 100% forbidden. The selection rules aren't obeyed all the time. So the molecule isn't very likely to emit light and fall down from the triplet state to the singlet state. It can happen rarely. It does happen very infrequently. So in fact that is what happens eventually is the molecule will make a vertical transition from this vibrational ground state of the triplet to an electronically excited state of the singlet below it. That step is the step that we call phosphorescence. That because it's very slow, typically doesn't happen any faster than milliseconds depending on the molecule and may be more strictly forbidden in some molecules than others. So it might happen as slow as many tens or hundreds or thousands of seconds as you know from using glow in the dark stickers or stars that you put on your bedroom wall as a child or whatever, you charge those up with light and then they glow for perhaps the next 15 minutes until the light fades. So that phosphorescence process is the slow release of light. It's slow because it's a spin forbidden process. Other than that it's very much like fluorescence. Excite the molecule with a high energy photon. Some vibrational relaxation occurs. Then emission occurs that we call phosphorescence. It's phosphorescence only in the circumstance where we've had this non-radiative intersystem crossing that gets the molecule stuck to where its only option is this spin forbidden transition which will happen very slowly. And then of course after that it will very rapidly vibrationally relax down to the true vibrational ground state. So step six, that vibrational relaxation step again occurs very rapidly. So the difference between fluorescence and phosphorescence is phosphorescence involves this spin forbidden emission but in both cases the emitted photon is much or at least somewhat lower in energy, lower in frequency, longer in wavelength than the incident photon that caused the excitation process.