If the nucleus disintegrates before electrons can cluster around it, you're not really in the realm of chemistry any more. Chemistry is all about those electrons.
It belongs in the group of noble gases, together with helium, neon, argon, krypton, xenon and radon. Like radon, it is unstable, but also like radon it is widespread in nature as a product of radioactive decays.
The element with Z=0 has multiple isotopes, like any other chemical element. Unlike for any other element, the possibility of gravitational stabilization makes the number of its stable isotopes potentially infinite.
The neutron stars can be seen as belonging to the isotopes of the chemical element with Z=0.
Their concentration is the result of the equilibrium between neutrons that decay into proton and electron pairs and proton-electron pairs that recombine into neutrons.
The complete neutron star still behaves like a giant nucleus with null electric charge, i.e. with Z=0.
From a big enough distance, there is no essential difference between neutrons and the neutral atoms of any noble gas. They all are neutral particles which do not react chemically.
The weak van der Waals forces between the atoms of the noble gases decrease from radon to helium and neutron fits in this progression. At extremely small distances between neutrons, weak attraction forces appear between them, which are analogous to the van der Waals forces generated by residual electromagnetic interactions, but they are generated by residual strong nuclear interactions.
A positive hydrogen ion has 0 electrons too, the same as a doubly-ionized helium atom, triple-ionized lithium atom, etc.
The relationship between neutrons and these ions is the same as for instance between helium and lithium ions, beryllium ions, boron ions, etc.
Calling a neutron as the limit case of an atom is a choice, but this choice simplifies many descriptions of things related to atoms and ions, in the same way as including zero in the cardinal numbers simplifies the descriptions of many things related to numbers, because there is no longer any need to describe separately some special cases.
However, in each island of stability the most stable element is much less stable than the most stable element of the previous island of stability. Therefore in most higher islands of stability the decay times will become too short.
It is possible and rather likely that only the first undiscovered island of stability may contain relatively long-lived elements, e.g. with half-lives over one second.
An island of stability finishes at bismuth, which is radioactive, but which has a huge half-life. The next island of stability contains the long-lived thorium and uranium and the still relatively long-lived neptunium and plutonium, after which the half-lives decrease very quickly.
Whichever will be the longest-lived elements of the next island of stability, their half-lives will be many orders of magnitude smaller than those of thorium and uranium.
Nevertheless, it was usually supposed that 126 is the next magic number for protons, in which case it has not been reached yet. Other possible values, from more recent computations, are 122 and 124, also not reached yet.
Moreover, the isotopes that are the most stable for the already synthesized elements are expected to have more neutrons than in the isotopes that have been successfully produced. So it is not impossible that an "island of stability" might have already been reached, but only with isotopes that have so few neutrons that they remain outside the zone of stability.
So clearly there is a limit. Either bounded by the point where gravity becomes dominant or when you get a black hole.
What happens in neutron stars is somewhere between nuclear reactions and quantum effects. Both of which are decidedly not "chemistry" in the way most people use that word.
More generally, only normal atoms can undergo chemistry. All of chemistry depends on the arrangement of electron orbitals. Once you leave that domain, you're in an entirely different field of physics.
[1] https://en.wikipedia.org/wiki/File:Binding_energy_curve_-_co...
In other words, energy required to break them apart.
There is a theoretical upper bound on the mass of an elementary particle at which it will collapse into a black hole. Fundamental particles can not be heavier than the Planck Mass, and Atoms should have a corresponding value at which they will likewise collapse into a black hole.
Black holes do not satisfy even the loosest definition of an element.
It may be difficult to predict just how far we can go in a lab, but the existence of black holes means there must be some limit.
The macro stars and the micro. I for sure thought that 118 was the limit, and again, this has been a life long interest of mine.
I have the isotope chxart on the wall at home.
P.s. kudos for paying attention in school.
P.p.s extra thanks the people who kept the Laurence hall of science going, and it's periodic table working.
[1]: https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
(It's not as if the speed of electrons would *exceed* c above Z=137; it just approaches it asymptotically. The 1/137 factor comes from the non-relativistic approximation (simply, the plain Bohr model [0])).
Imagine 500 years in the future when we have laptop particle accelerators... We may have whole diffent reality around 'strange'.
The line from the remake of 'the man who fell to earth.' "He has miscalculated the chirality."
The operating definition has been "a list of all elements that humans have discovered and/or made". By that definition, it is not currently infinite, nor will it ever be.
If instead you define it to mean "all elements that might theoretically exist under all theories of physics that are not currently definitively ruled out", then it may be it infinite. But that's not the normal definition.
I think it is clear what question is being asked here. There will be a limit on the maximum size of a nucleus stable enough to count as an element, as there are a couple of effects which, at some point, will be insurmountable (and which are also responsible for an isotope of lead being the largest stable element.)
One is that the electrical repulsion of the protons is long-range, while the strong nuclear force binding the nucleons together is short-range. To simplify quite a bit, in a large nucleus, each proton is being repelled by every other one, while it is being bound only by its neighboring nucleons.
The second effect prevents this being worked around by adding more neutrons, as one reaches a point where it is energetically favorable for a neutron to convert to a proton via beta decay.
As mentioned by others, there is likely an 'island of stability' around the largest elements created so far, but this is, at best, only a brief respite from the inexorable effects described above.
The estimates of the half-live of any given element on the island of stability ranges over several orders of magnitude. That being so, it seems unlikely that there is any clear idea which isotope is the largest possible in this universe.
Neutron stars are, of course, very large agglomerations of nucleons, but it seems pointless to call them elements (and there is an upper limit on their size, anyway.)
We give too much importance to the "Periodic Table". It's just a man-made microlang. Nature is unconcerned with it. There is much more beyond it.
P.S. While I'm criticizing the PT, might as well mention that I think we've probably done people a diservice by giving misnomer names like "Hydrogen" and "Oxygen" to these elements, which is completely disconnected from the mathematical beauty and patterns that those names represent.
Wikipedia: Oxygen
> Lavoisier renamed 'vital air' to oxygène in 1777 from the Greek roots ὀξύς (oxys) (acid, literally 'sharp', from the taste of acids) and -γενής (-genēs) (producer, literally begetter), because he mistakenly believed that oxygen was a constituent of all acids.
Hydrogen comes from ‘water’, which contains hydrogen and oxygen.
So, since all acids must have Hydrogen, Oxygen is actually a better name for Hydrogen. This then leaves the name Hydrogen free for Oxygen.
Singtium and Octium, perhaps.
At some point it becomes "quark matter" and might exist in collapsed stars.
Atoms are much bigger than subatomic particles, so they have to live even longer in order to exist.