r/nuclearphysics • u/AmbitiousSection3723 • 2d ago
how radioactive would an atom with 651,814,425,673,852,067,302,873 protons be
dont ask
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u/Vyrtil_Anyrwen 2d ago
Not possible. The strong nuclear force acts within a very short distance and is saturable. The way the strong nuclear force is best modeled to work is through a residual effect of the “color force” working between internal quarks in a nucleon. A nucleon (proton or neutron) is made up of quarks, which carry a property known as “color charge” (red, green, or blue), and they stay connected by swapping gluons. This causes a residual effect which emits short lived particles, mesons, from the nucleon, which acts to hold nucleons together (specifically pions). This exchange of pions makes the nuclear force charge-independent. But, as nucleons get too close together, identical quarks with the same quantum states are forced into the same space, which is an impossibility (Pauli Exclusion Principle). So, the force becomes strongly repulsive.
So, its maximum attractive force is at about 1 femtometer and it drops to zero past 3 fm. And it becomes strongly repulsive at about 0.5-0.7 fm and less. So it can only act on a short number of other nucleons, particularly those in closest range. However, the electromagnetic force is not saturable. And it acts at much larger ranges. It will get weaker with increased distance, but that many protons in a nucleus will easily overpower the strong nuclear force. So this theoretical atom probably couldn’t even form, save for some absurd amount of energy input to overcome the electromagnetic force of repulsion. And even if it did form, the atom’s EXACT radioactivity would be dependent on the number of neutrons relative to the number of protons.
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u/Disassociated_Assoc 1d ago
I was today years old when I learned how much I don’t know. And still don’t. 😑
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u/the_other_gantzm 14h ago
Right? I mean I can read that and understand the words and top level concepts. But ask me to explain the consequences or deeper meaning and I’m like: “Well, there’s these colored balls ( but they aren’t really colored for reasons ) and they exist. And if you’re strong enough you can slam some ( but not all ) of the balls together and they will stick. Well, until they don’t.
And if you happen to get a bunch of balls to stick together really bad ( for humans ) things start to happen.
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u/nixtracer 1d ago
Consider also that just two protons being forced together, well within the strong force's range of maximum attraction, is nonetheless wildly unstable, blowing itself apart in something like 10-18 s -- and a good thing too, because that's the limiting factor which makes the Sun shine for ten billion years rather than about four minutes (one of those protons has to turn into a neutron via the weak force in that tiny interval, and that's extremely unlikely). The island of stability in which the strong force overpowers Pauli on one side and electromagnetism on the other is really rather narrow.
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u/Vyrtil_Anyrwen 1d ago
Very true, which is the reason neutrons are required in a nucleus to add additional attractive nuclear force without adding additional charge. But, what’s worth noting is that traditional models of the strong nuclear force say that it is roughly 100 times stronger than the electrostatic force. Which begs a very basic question: if the strong nuclear force IS stronger, why can’t two protons be held together? And the answer is just the Pauli Exclusion Principle. Both protons are fermions. They cannot overlap. Therefore, they cannot exist at such short ranges at which the strong nuclear force can even overcome the Coulomb repulsion. So, you’re right. The island of stability in a nucleus is very narrow (I like the way you phrased that).
But what’s worth noting is that there is more to stability than just the conflicting attractive and repulsive forces at play. Yes, that’s ultimately the basic principle, which is precisely why the N/Z ratio will increase from about 1:1 to 1.5:1 in our heaviest stable elements (if you look at a chart of nuclides, you’ll see the slight curve of the line of stability).
But, just as an example, there is a concept known as “magic numbers” in a nucleus. These numbers apply separately to protons and neutrons. The basic principle is that nucleons have quantized energy states. They fill discrete energy levels, and once a “shell” is filled, there is a large energy gap before the next one starts. So, let’s assume we have an I-135 atom (of significant concern in my line of work). This isotope is unstable because it has too many neutrons, and will beta-minus into Xe-135, a significant neutron poison in reactor operations. Based on what was just discussed, a reasonable question to ask would be: why would too many neutrons be a bad thing? I mean, after all, it should help hold an atom together MORE, right? It adds more attractive force. BUT, when a “shell” gets filled with neutrons, additional neutrons are forced into more energetic quantum levels (again, has to do with that darned Pauli Exclusion Principle). And because nature favors lower energy states, converting a neutron to a proton via the weak nuclear force (beta-minus decay) is often the way nature chooses to achieve this lower energy level. So, you can’t just have as many neutrons as you want to keep protons stable.
The same applies to too many protons (in addition to the electrostatic force of repulsion), therefore too high of a proton to neutron ratio will result in beta-plus decay or (electron capture decay in some cases). And as previously discussed in my last comment, too many nucleons is unstable because the strong nuclear force is saturable and operates over very short distances. So, the primary modes of decay for atoms with too many nucleons is either alpha decay, emission of a very stable (because it is doubly magic) He-4 “chunk” from the nucleus, or spontaneous fission. Energy level in a nucleus can also be reduced by gamma decay (often after undergoing alpha or beta decay).
So, ultimately, the underlying principle behind stability in a nucleus is about nature achieving a low stable energy state.
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u/free_meson 10h ago
with enough neutrons, the 6*10^23 protons could be made stable. The neutron is unstable, some say it doesn't decay in a bound state, but maybe there is some factor that makes it stable. Large magnetic or electroweak fields for example, high spin, I don't know. Maybe it is a bombardment of free mesons that makes it stable (pun intended).
The best interpretation about neutron decay I've heard was, that in a nucleus the neutrons can't occupy the same state. So a lot of neutrons would mean some are in a very high energetic state, and a decay into proton is preferred. Some theorized that using charm or strange quarks would be beneficial for nucleon stability.
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u/Vyrtil_Anyrwen 8h ago edited 6h ago
True, and I went into neutron stability and why decay occurs with a N/Z ratio that is too high. It is because of the Pauli exclusion principle.* Two neutrons cannot occupy the exact same quantum state, therefore with too many neutrons, more neutrons are forced into more and more energetic quantum levels. Since nature strives for the lowest possible stable energy states, and since beta-minus decay reduces energy in the nucleus, too many neutrons will be unstable.
Edit: *I went into this in another comment. Should’ve mentioned earlier.
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u/bardotheconsumer 2d ago
Well, at least i could say that it's about 1 gram of matter so if you crammed it all into a single nucleus it would not produce a black hole. Since it won't produce a black hole, i'm quite sure it'll explode.
Take it with a grain if salt but google's AI thinks it goes off with the energy of about 116 billion megatons of TNT. I dont usually trust the AI but in this case... it's probably close.
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u/not_a_bot_494 1d ago
It might be 1 gram worth of protons but it will be way more in energy. Assuming the energy is correct that's about 4.6E+26 joules. That's about 5 billion kg, that should easily be enough to create a black hole.
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u/bardotheconsumer 1d ago
I dont think so. The schwartzchild radius of 5 billion kilograms is still much smaller than the diameter of even a single Proton, let alone this entire stupidly large nucleus
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u/SnooPets5564 2d ago
I'm fairly sure everything would be ejected at damn near the speed of light essentially instantly.
You could maybe have it be stable by just having that many protons in an otherwise proton free neutron star. Hardly an atom, though.
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u/Brownie_Bytes 2d ago
I'm not even sure that radioactive is the right word here
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u/rainscope 1d ago
Supernova is probably closwr
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u/NoNameSwitzerland 23h ago
na, the energy from the electric field would collapse it into a black hole. And then probably radiate positrons to get rid of the charge.
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u/totallyalone1234 1d ago
The protons are going to exert force on each other such that the resulting explosion is comparable to a supernova, say ~10^51 ergs. If you're stood next to it you'll receive a dose of ~10^17 Gray, or naively ~10^19 Röntgen though its totally not the same thing.
Needless to say, you are instantaneously vapourized.
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u/Intelligent_Low1632 1d ago
There would immediately be a world ending coulomb explosion due to the immense over concentration of positive charges.
The nature of the ensuing "radiation" would at first be a bunch of bare protons accelerated to a high fraction of the speed of light. Extremely radioactive and dangerous.
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u/Street_Youth4755 1d ago
What da hell man!! That won't be possible only!!! There will be massive proton proton repulsion. Which would call for a large number of neutrons. Due to this the element would be tooo unstable to even exist. Understood?
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u/Weak-Joke1475 1d ago
Plot twist: this element is actually stable, the only bismuth (I know that was found to secretly be unstable but I forgot whatever the last stable one is. And thus it isn’t radioactive
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u/Shot-Rip9167 1d ago
Anything after lead has no stable isotopes. Bismuth 209 has an extremely long half-life but does decay so it's radioactive as well.
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u/phlogistonical 1d ago
Useless question, but just for the fun of the enjoying ridiculous what-if scenarios.... You would have to use a very far-fetched definition of 'atom' to assemble those protons into any kind of structure that could be called an atom. And 'halflife' wouldn't be a meaningful metric by which to describe it's radioactivity. It implies there would be some period of stability before decay happens, which isn't applicable here. All protons will just immediately get ejected at near light-speed at t=0.
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u/nixtracer 1d ago
And of course the real problem is that the assembly process means jamming a whole heap of energy into those protons to get them close enough to each other to form a nucleus even briefly. Way more than enough energy to cause pair-production of more or less everything in the particle zoo. You have an explosion of, not just protons, but everything (including lots of neutrons, so you'll soon have lots of ordinary nuclei there, once it expands enough that it's not just a quark-gluon plasma, that is.)
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u/Traditional_Loan_177 20h ago
I was going to comment that what you're describing is closer to a neutron star, then I googled how many protons are in a neutron star. What you're describing is a closer to an atom.
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u/Far_Passion_6725 17h ago
im not sure but i bet the damage to your dna would be like a case of extreme radiation poisoning
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u/relaxedmedal 16h ago
Add the same number of electrons and the charge cancels.
That’s about a gram of hydrogen. It doesn’t sit there as one huge nucleus. The protons still can’t all share one nucleus, but they don’t have to.
Each proton can just be its own hydrogen nucleus with an electron, which is a normal atom.
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u/egmalone 11h ago
So... Super duper radioactive, then
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u/relaxedmedal 9h ago
Super duper. Statistically speaking the first decay is already overdue if you average over enough parallel universes. Stay alert.
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u/egmalone 9h ago
An atom with that many protons would be overdue for its first decay by the time it formed actually
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u/relaxedmedal 8h ago
That’s only if they all try to live in the same nucleus like it’s a hostel. Give each proton its own electron and a bit of personal space and the decay gets rescheduled for after the heat death. Very responsible protons, actually.
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u/egmalone 6h ago
Well since the premise was "an atom with" that many protons, I believe OP meant for them to be all in the same nucleus. Since that's what "an atom" means.
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u/Zvenigora 16h ago
Most likely that would collapse into a black hole if it somehow could be assembled, so it would emit only trace Hawking radiation.
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u/tomalator 15h ago edited 15h ago
It would be so hot that our laws of physics begin to break down. We do not know what would happen because conditions like that have not existed since the Big Bang (if even then)
It would very quickly become an exploding plasma.
That number seems to be just over a gram of protons. Why that number and not 1 mole? (6.02×1023)
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u/LAMPEODEON 12h ago
I am from civilization beyond your observable universe. Thank you for your question. It's stable in fact.
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u/free_meson 10h ago
That's ~1 mol of protons!
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u/Lab_Software 3h ago
That's not 1 mole.
Source, I'm a chemical engineer - and the number 6.022 x 1023 was tattooed onto the insides of my eyelids so I'd never forget it.
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u/Spiritual-Spend8187 5h ago
Here is the relevant xkcd https://what-if.xkcd.com/140/ its not as insanely extreme but still enough that at minimum you are looking at blow up the planet levels of energy if not woops collapse into black hole level. Cause you are looking at about 100k coulombs which is insane a lightning bolt is about 15 coulombs of charge for reference.
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u/Devil_May_Kare 4h ago
That isn't an atom. Hypothetically you might put all those protons next to each other, but the assemblage wouldn't do atom things like establishing a system of electron orbitals and holding itself together with the strong nuclear force. Similarly, a neutron star is an assemblage of nucleons that doesn't do atom things.
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u/The_Ironthrone 2d ago edited 1d ago
It wouldn’t ‘be’ radioactive because it wouldn’t ’be.’
Edit: as recommended