Incoming links: Isotope
Most of the helium in the Earth's atmosphere comes from alpha decay, since helium is lighter than air and naturally escapes out out of the atmosphere.
Wiki mentions that alpha decay is well modelled as a quantum tunnelling event, see also Geiger-Nuttall law.
As a result of that law, alpha particles have relatively little energy variation around 5 MeV or a speed of about 5% of the speed of light for any element, because the energy is inversely exponentially proportional to half-life. This is because:
- if the energy is much larger, decay is very fast and we don't have time to study the isotope
- if the energy is much smaller, decay is very rare and we don't have enough events to observe at all
- youtu.be/_f8zeEI0oys?t=796 George Gamow and Edward Condon proposed the quantum tunnelling explanation
- youtu.be/_f8zeEI0oys?t=1725 worked out example that predicts the half-life of polonium-210 based on its emission energy
A nuclear reactor made to produce specific isotopes rather than just consume fissile material to produce electrical power. The most notably application being to produce Plutonium-239 for nuclear weapons from Uranium-238 being irradiated from Uranium-235-created fission.
Stable isotope.
Highly radioactive isotope of caesium with half-life of 30.17 y. Produced from the nuclear fission of uranium, TODO exact reaction, not found in nature.
The fucked thing about this byproduct is that it is in the same chemical family as sodium, and therefore forms a salt that looks like regular table salt, and dissolves in water and therefore easily enters your body and sticks to things.
Another problem is that its half-life is long enough that it doesn't lose radioactivity very quickly compared to the life of a human person, although it is short enough to make it highly toxic, making it a terrible pollutant when released.
This is why for example in the goiânia accident a girl ended up ingesting Caesium-137 after eating an egg after touching the Caesium with her hands.
caesium-137 decay scheme
. Source. 
You label cells with isotopes rather than fluorescent substances. Vendors claim that this allows much wider N-way sorts, e.g. 2022 Fluidigm claims around 40/50, because the fluorecent spectrum is too wide to do much more than 7/8 way splits.
Plutonium-240 is a contaminant.
This isotope shows up as an inevitable contaminant in Plutonium-239 for nuclear weapons, because it emits neutrons too fast and makes it harder to assemble the critical mass without fizzle.
It is the presence of this contaminant that made implosion-type fission weapon a necessity: Section "Gun-type fission weapons don't work with plutonium".
The only isotope found on Earth because it occurs as part of the uranium 238 decay chain, i.e., it is not a primordial nuclide.
Interestingly it is a bit less stable than other isotopesL such as Polonium-208 (3 y) and Polonium-209 (124 y), but those aren't in any Earthly radioactive chain so they don't show up on Earth.
For nuclear weapons you need a certain level of isotope purity of either plutonium-239 or uranium-235.
And the easiest way by far to achieve this purity is to produce plutonium-239 in a breeder reactor, which allows you to get it out with much cheaper chemical processes rather than costly isotope separation methods.
fissilematerials.org/ summarizes stockpiles and production status. 20224 Archive.