Inspired by this thread:
After viewing that thread I found this
which shows elements up to 218.
Now I know that only half of that has actually existed at any point, but is that the theoretical upperlimit of elements. Is there a point where physics just won’t allow an element to exists or can they just go on until it’s so heavy it form a black hole?
(Your second link is broken. Here it is.)
There are a lot of complicated quantum effects at work in holding an atom together. Someone more qualified in physics might correct me on this, but I don’t know if we can calculate, even roughly, a theoretical upper limit.
As a general rule, larger atoms are less stable than smaller atoms. A lot of the elements towards the end of the current PT disintegrate very rapidly. It wouldn’t surprise me if 250 proton atoms were impossible. Then again, it wouldn’t surprise me if atoms with 400 protons are possible, however fleeting.
Short answer: dunno. Sorry.
think about it: Can a man juggle 3 balls? Probably. Can he juggle 10? Possibly, but he’d have to be a pro. Can he juggle 7,000? Almost certainly not. Same with atoms.
The analogy is flawed. Atoms are not balls.
Superheavy theoretical atoms with 110 protons and 175 neutrons or so may exist.
Islands of Stability
The answer is either “no upper limit” (until you get to black holes), or “some of the elements already on the table don’t exist”. As you get heavier and heavier, the lifetimes (generally) get shorter and shorter. Eventually, you’d get up to things that only last for nanoseconds or picoseconds or grouchoseconds or whatever, and you might be tempted to say that those don’t “really exist” in some sense. But then, if you’re going to use that standard, does an atom that lasts for milliseconds “really exist”?
Would a neutron star with assorted sprinkled protons count as a huge atom nucleus?
There was a recent series of sci-fi novels where the unobtainium was explained away as the product of the discovery of a group of stable elements (with amazing properties) in the range of atomic number 900.
Not Groucho, but Zepposeconds hit the Marx.
Personally, I wouldn’t, since they’re bound primarily by gravity, not by the strong force. But for the record, neutron stars have more than a sprinkling of protons: Approximately 10% of a neutron star’s mass is protons (with a corresponding number of electrons to keep the charge neutral, of course).
Not doubting the influence of gravity, but do we know that they are not bound by the strong force as well? How do they compare as “glue”? Is gravity an issue in a nucleus? (the masses may be small, but so are the distances)
The gravitational force between two charged subatomic particles (and almost all of them are charged) is less than 10[sup]-40[/sup] times the electrostatic force between them. This is true regardless of distance, since gravity and electrostatics fall off in the same way with distance. The only reason that gravity dominates at planetary and larger scales is that most planetary-sized objects are neutrally charged, or very close to it: The fact that there’s two different kinds of charge, and that they attract, guarantees that. But there’s only one kind of gravitational “charge”, and they attract, so large masses tend to accumulate.
The strong force, by contrast, does not fall off in the same way with distance: It falls off much faster, meaning that, at very short distances like the interior of a nucleus, it’s stronger than electromagnetism, but at distances even as long as the distance from an atom’s nucleus to its electrons, the electromagnetic force is much stronger than the strong force. What this means is that if you start off with two protons and try to push them together, at first they resist, due to electromagnetism, but if you can get them close enough, they can attract and fuse together into a nucleus.
But back on topic, because of the way the strong force works, any given neutron is only going to be strongly interacting with the neutrons right next to it, or maybe a few over, but it’s gravitationally interacting with other neutrons throughout the star. So even though gravity is inherently so much weaker, in the end it all adds up, and so dominates.
Wait, shouldn’t there be an upper limit? As you add more and more protons to the nucleus, the innermost (1s) electrons are going to have to move faster and faster to avoid being pulled into the nucleus. I know that, in the Bohr model (one proton and one electron), that electron is moving at 1/137th of the speed of light, but I’m pretty sure you can’t say that the electrons in helium move at 2/137th of the speed of light. But even so, shouldn’t there be some upper limit based on the approach of the core electrons to the speed of light?
Then again, I suppose all bets are off if you’re making hugely cationic elements (nuclei only), but I imagine that’d involve a new suite of problems suited more for a nuclear physicist than a chemist.
Fascinating. At what distance does gravity start surpassing the strong force? Would that be the maximum radius of a nucleus as such? What ballpark atomic numbers are we talking about at this point?
For my part, I’m wondering if the sheer size of the nucleus wouldn’t impose an upper limit. Given the facts as Chronos explained them, it seems that at some point, protons at one point in the nucleus are going to be so far from some of the other protons that the strong force and the electromagnetic force will cancel. Get much larger than that and the whole thing would become unstable. Or am I reading too much into it?
RR
The Bohr model is not an accurate model of the Hydrogen atom in even a rough sense. It’s not correct to say the electron is moving at 1/137th of the speed of light. Here’s an image of the orbitals (taken from here). The red and blue represent the wavefunction being positive or negative at that location. The top row hows the S-orbitals. The next two rows show P orbitals (there’s a third just like the first two, but rotated), and the rest are D orbitals. A good periodic table will list the orbitals that are filled in the ground state for each element.
Note that there are no planet-like orbits there.
That’s not really known, since there’s a lot about the details of the strong force that we don’t know. But we can get a rough estimate from approximating it as a pion-mediated Yukawa potential, which would put it at somewhere around 10[sup]-13[/sup] meters. This is about 100 times the diameter of a proton, so assuming (probably incorrectly) that all nuclei have about the same density, that would correspond to an atomic mass somewhere in the vicinity of a million. Of course, gravity is still negligible at those scales; it’s just being dwarfed by electromagnetism, instead of the strong force.
Quoth RiverRunner:
Well, yes, but all of the upper elements are unstable. The fact that a nucleus is unstable doesn’t mean that it can’t exist; it just means that it can’t exist forever.
For stability or even relative metastability (unstable, but more stable than ‘neighboring’ isotopes), it’s all but essential that a large percentage of the nucleus be composed of neutrons, subject to the strong force but not to electromagnetic repulsion, and therefore ‘buffering’ the E-M repulsion of the protons. There is only one stable isotope that is more than 50% protons, and that a rare one: Helium-3. AFAIK, the only isotope composed solely of more than one proton, Helium-2, has a half life on the order of 10[sup]-27[/sup] seconds. Stable isotopes of 50% protons and 50% neutrons (e.g., He-4, C-12, O-16) exist among the lighter elements, but I believe top out at Neon-20. All stable isotopes above that have a relative preponderance of neutrons. For example Pb-208 has 82 protons and 126 neutrons; metastable U-238, 92 protons and 146 neutrons .
There is quite likely a maximum number of protons beyond which no quantity of neutrons will serve to produce an isotope with even femtosecond stability. And as time continues to be fractionated to the point where something cannot be measured even theoretically, the issue of its existence becomes a question, not of subatomic physics, but of metaphysics.
Is a life of 10^-27 seconds a life at all? That sounds like the time it takes things to fly away. What makes us consider they were a thing at some point, and not just two items put together and flying away the instant we let go?
If Chronos’ numbers are anywhere near correct, a nucleus with a mass of 1M should be able to hold a rather large number of protons mixed in there.
Is a “ball” of neutrons stable by itself? Say 100 neutrons with no protons. Is there a name for those?
Well, if you’re going to argue that, then you’ve got to draw the line somewhere. How short does a lifespan need to be before it doesn’t count? I don’t think there’s any particularly good answer to that.
I think that you’re misapplying that number. For that matter, I think almost any use of that number would be a misapplication: That’s just the nucleus size where gravity becomes comparable to the strong force, but comparing gravity to the strong force is almost never going to be relevant for anything. For stability of an atom, you’d want to compare electromagnetism to the strong force, which (to the precision of the back-of-the-envelope method I used) corresponds to the atoms which, experimentally, are indeed unstable.
Almost certainly not. At least, nobody’s been able to make one, and nothing that we know about the strong force suggests that they should exist. Quark nuggets (agglomerations of a great many quarks, the constituents of protons and neutrons) may or may not exist, but if they do, the quarks aren’t organized into nucleons-- It’s just one big sea of quarks.
