A single atom of jumbonium, an element so rare the nucleus alone is worth more than $50,000.
How much more?
100,000. That’s why I hid it here, under my mattress.
I believe the limitation is in atomic weight, not in electron orbital speed. I have heard the orbital speed statement but I don’t understand that since from a quantum standpoint electrons are not moving in a continuous path like billiard balls or satellites.
I thought the limitation of around atomic number 137 came from the short-range strong nuclear force being unable to bind the electrostatic repulsive force of protons in such a large nucleus.
Re electrons being unable to distribute themselves over a mile-wide orbital, that orbital only exists on a quantum scale, so the concept has no meaning. However electrons apparently can travel at infinite speed during quantum tunneling:
They aren’t like billiard balls or ping-pong balls or any macro-level physical entity you have ever experienced. They do not follow intuitive rules of logic we’re accustomed to in the macro world.
Regardless of stability concerns, there can’t be an infinite number particles in the universe, so finite.
If we are not concerned about stability, then the periodic table definitely is infinite, since for any element N, there is always a heavier element N+1.
John Mace’s point stands.
137 is where the 1s electrons would have to move faster than the speed of light in the Bohr model of the atom. The Bohr model is not an accurate model even before you get there, so 137 doesn’t represent a real physical limit of any sort.
Extended periodic table - Wikipedia is a good read for anyone interested in this, it gives a decent overview of the topic.
So does the more serious one that I made several posts before John Mace made his:
Yep. Almost zero chance - but worth signing just in case. 
In a way, any claim of an infinite character to any physical measurement is invalid. We offhandedly speak of an infinite universe, but…no. That simply cannot be. It can be vast, beyond any earthly comprehension, but if it is an actual physical entity, it cannot be infinite.
Impressive to synthesize it in sufficient quantities to be tasted!
I prefer to think of myself as a trend-setter…
I’m definitely out of my depth here, so forgive me if I flub this up… But if you had an electron in a mile-wide orbital, wouldn’t that require horrible levels of momentum or energy uncertainty, to make up for the incredibly vast positional uncertainty that this imposes? i.e., it isn’t the “speed of passage” that kills this idea, but the ability of an electron being anywhere in a cloud…a blessed mile wide, with all that implies under Uncertainty Theory.
But is that so? I’m not aware that an infinite universe violates any physical law; and it’s certainly a valid possibility under the standard model, cosmologists routinely discuss the matter as open and undecided. I grant that it’s a weird idea, but is it any weirder than a black hole? Or, come to that, QM?
We know of no physical law that would prohibit an infinite universe, but such a universe would also be indistinguishable from a very large but finite one.
And the Uncertainty Principle never puts any upper bounds on uncertainty. An uncertainty in position of a mile is perfectly allowable, and would be even if you had an extremely precisely-known momentum. Huge uncertainties in both? No problem at all.
This. The declaration is not testable.
But I go further and say it’s wrong, because it is applying a mathematical concept for “without limit” to physical realities, where it cannot be realized meaningfully. This usually comes up in theological disputes…
I may be screwing this one up, but just because the nucleus is a mile wide doesn’t mean the 1s orbital “is a mile wide”. Would not the electrons of an atom this big “orbit” (mostly) inside the nucleus?
It’s certainly testable - it’s falsifiable. If we do eliminate all “small” finite universes, and we are left with the remaining possibilities of a large finite universe and an infinite universe, with no way to distinguish between them, then we have no more reason to dismiss the infinite universe than to dismiss the very large universe.
And it’s begging the question to say that infinity is a mathematical concept but not a physical one - whether there is a physical infinity is precisely the moot issue.
I’m somewhat playing devil’s advocate here, obviously. But i’m finding it hard to see solid grounds for just dismissing it.
By “not testable,” I mean the same as what you just said: there is no way to distinguish between the two. There is no test we can apply to a very big universe to assure us that it is, in fact, infinite…and no practical test we can apply to a sufficiently big universe to assure us it is not, in fact, infinite.
There can always be constructed a universe so large that its inhabitants cannot distinguish it from an infinite universe.
I think we’re actually agreeing here.
Yes, the Periodic Table is finite. The reason heavy nuclei are unstable is that they are large, and the strong force that holds them together has a finite range, while the electromagnetic force that blows them apart does not. For a large nuclei, protons that are momentarily on opposite sides of the nucleus may be so far apart that the electromagnetic repulsion between them is greater than the strong force holding them both in the nucleus. In that case, the atom decays. Actually, it decays even faster than that, because if the electromagnetic repulsion is just a bit less, the protons can tunnel out of the nuclei.
The bigger the nuclei, the more likely this situation happens, and the faster (on average) the nucleus decays. The more unstable it is. Now, clearly there must come a point where the nucleus is absolutely unstable – where some protons will always feel more electromagnetic repulsion than strong force attraction, and where therefore the nucleus will not stay together for even an instant tending towards duration zero. It would obviously be true for a nucleus that is, say, 1 micron across. It would not hold together for any finite time. Even if you got all the protons and neutrons into the prescribed volume, they would exit it without stopping – you would have something better described as a momentary collision of nuclei than as a single nucleus, even for an instant.
That’s the upper limit. You’d think it would be possible to calculate this limit, but alas you’d be wrong. The problem is that calculations with the strong force and a lot of nucleons are very, very hard. Our current theories say 3 quarks per nucleon, so a nucleus of weight 300 = 900 quarks, which is well beyond the ability to do precise strong-force calculations. Remember this has to be done relativistically, too, given the energies involved. In fact, one of the best reasons for trying to make very heavy nuclei and measure their properties experimentally is that it serves as a check on methods of doing these kinds of calculations.
I’m sure there are various estimates of the upper limit out there, and you could find them with some effort. But no one has a number that everyone agrees is right. I think almost everybody thinks its less than, say, Z=200. But I suppose we could be surprised. Indeed, it would be very interesting to be surprised.
By the way, you can’t build a honking big “nucleus” out of pure (or nearly pure) neutrons, because they’re unstable and decay into protons and electrons unless under sufficient pressure, which you can only provide in a neutron star. So there’s no such thing (so far as we know) as neutronium in globs smaller than star-size.
Also, while Chronos’ argument is elegant, as a chemist I reject it. Electrons are certainly of profound importance in chemical behaviour, but that is not all there is to it. The most obvious counterexample is H+ – a single proton, zero electrons – which exhibits a wide and important range of chemical behavior. I do agree you could build an “atom” that consisted of some magical central object that had the same charge and mass of a nucleus, plus electrons around it. But of course that would be functionally an atom in everything but the details of its nuclear structure (if any). Although, even there, there is some subtlety, as there are interactions between nuclear spin, and between nuclear and electron spin, that have (slight) chemical relevance. A weird example is the difference between ortho- and parahydrogen.
Well obviously the first atom is hardly going to be used to indicate what happens at the tail end… we can take hydrogen as pathological ?
What isn’t pathological is that plasma has the electrons totally leave all the nuclei, you can have “Si +14”, as in just the silicon nucleus with no electrons whatsoever, and its still silicon and it will then regain its electrons when it cools down.
What we are finding is that the mass of the nucleus could affect the chemistry, but basically the complex chemistry (acids, bases, polymers,etc) occurs with atoms with just one neutron count in the stable atom, and where the natural occurring neutron counts of the stable species vary, its the heavier ones, so less significant , so what about a neutron or two ? and anyway the trailing end is all metallic… its useless to extrapolate from the heavy metals, as there is really no trend to extrapolate… a flat line provides no information as to where a change occurs. (a second line would have to intercept it, but thats not a known thing… such as a higgs field…very wide error margins, which combines with the large number of particles… meaningless … no resulting formula…)
The speed argument is garbled, just a mere reference, so you didn’t understand it.
A better way to understand it, due to the sum of Pauli and Heisenburgs principles, the electrons remain out at large diameter, and don’t neutralise with the protons. The other way, there is a limit to the size of the proton and neutron nucleus, or else the electrons will neutralise a positive quark in the nucleus…
So if the OP’s question was, is there a maximum size of the the proton, neutron nucleus, the answer is yes, it must stay inside the smallest electron shell diameter…
Of course its possible that it may have to stay well clear, due to tunneling, but calculating that requires an exhaustive list of the particles, properties, and modes of stability that might occur …
(given there’s such a long list of quarks and their properties… )
Did you know that while the nucleus is said to be made of neutrons and protons, its actually made of sets of quarks, each set is made of three quarks, and the quarks are not stationary… one set exchanges a quark with another… effectively, a neutron changes into a proton when another proton changes into a neutron.
Well anyway, its not the OP’s question but if the nucleus did contain something like a higgs boson, then it may have a field that is far larger than the strong and weak nuclear force… and reach out to the electrons ? so actually affect the “chemistry” ?
Since the electron shell (ie atomic diameter) is 10,000 times the diameter of the nucleus, this doesn’t seem much of a limit. I thought the first limiting factor concerns strong force and nuclear stability which is vastly before any theoretical limit on nuclear diameter and inner electron orbital.
Re electron orbital velocity, my understanding was classical notions about electrons traveling at certain speeds don’t really apply in this domain. IOW from a quantum standpoint you don’t model an electron bound to a nucleus as an orbiting object. To have velocity there must be a displacement and position. The bound electron doesn’t have a defined position so velocity has no meaning.
From the quantum mechanical perspective the electron does not have a continuous trajectory. It’s not like a tiny orbiting moon which we could measure with a radar gun if we had one sufficiently small and sensitive. Therefore I don’t understand the reasoning about electron orbital velocity, unless that was a Bohr model simplification.
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The s orbitals are densest in the center, in the middle of the nucleus, and the 90% margin gets smaller as Z goes up. I’ve never heard anybody in chemistry circles say that the electrons don’t penetrate the nucleus. Maybe physicists know better. I don’t know why we should expect mile-wide orbitals in giant atoms. I think we’d see the opposite.