system
Given the following post, respond as if you're commenting on Reddit:
human
PARTICLE PHYSICS: What determines the amount of time between when an electron moves up an energy level due to being hit by a photon, and when it re-emits the photon and returns to it's original energy level?

Sorry about the wordy title. 

Also, please explain like I'm 5.
gpt
First, clarification. You question takes it for granted that a photon is reemitted. This is not always the case. Our poor electron is typically subjected to both *radiative* (photon emitting) and *non-radiative* (not directly photon emitting) relaxation pathways. We'll try to keep both in mind...


Ok, so now we've successfully excited an electron into an excited state. How long it will stay there depends on what we in the business call "system-bath coupling". Sound ambiguous? Read on...


The reason it sounds ambiguous is because it's a catch-all. Basically, anything perturbing the electron will give it a chance to go back down to its ground state. Some examples are in order:


* The electron is in an atom in the gas phase. It's lifetime can be seconds or longer if there's minimal external disturbance (magnetic fields from elevators whizzing by, RF signals from a wifi router, ...) and the internal pathways are all very slow (interaction energy between electron spin and nuclear spin is practically zero...).


* The electron is in a typical organic molecule. Remember non-radiative relaxation? Here's where it's important. Depending on how this electron is shared by atoms in the molecule, it may never reemit a photon, and instead excite some vibrations in the molecule. Those vibrations send the energy down the hierarchy into other vibrations, which eventually ends up as "heat".


Now, if this molecule is rather special (a naturally occurring fluorophore) or it was engineered by a chemist (!!), it might have minimal *non-radiative relaxation pathways*. The poor electron is just sitting in its excited state, doing nothing, until eventually it reemits a photon and goes home.


The take-home lesson is two-fold:

1. An excited electron relaxes by whichever pathway is fastest. This depends on what the system is (gas-phase atom, molecule, crystal) and what the external influence is (in a dense solution, in a hot oven, sitting in a magnetic field).


2. Fluorescence is usually a slow process. It will reemit a photon only if  there is basically no other option for how to dissipate energy.



(Why is fluorescence slow? Well, there are some "external influences" you can't get rid of, such as fluctuations in the electromagnetic field present even in a vacuum. These are the perturbing factors that cause spontaneous emission, such as fluorescence. But they're weak... usually weaker than any influence caused by neighboring molecules, internal vibrations, magnetic fields of elevators, etc...)