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Exploring the "Island of Stability": Can Enhanced Nuclear Shell Effects Lead to Long-Lived Nuclei Beyond Z=120?

There are currently 118 elements in the periodic table but could there be more. Maybe there's an infinite number and we could eventually discover unobtainium. But let's forget about unobtanium for a minute and take a look at good old ubiquitous carbon elements are defined by the number of protons they have.


Carbon

So carbon is carbon because it has six protons it also has six and a bit neutrons a bit because it has three naturally occurring Isotopes carbon 12 and 13 are stable but they're heavier C than carbon 14 is radioactive and has a half life of around 52,000 years. The half life is a measure of the time it will take for half of the atoms in a material to radioactively Decay that's how we do carbon dating. We just check how much carbon 14 is left in something compared to if it was new. Fortunately for us most carbon isn't Radioactive in 5,500 years is a pretty damn long time so we don't exactly consider carbon to be a radioactive element. As elements get heavier they tend to become less and less stable.

Period table graph Valley of stability

Each Square in this graph is a different isotope of every element we've ever discovered. This black line shows all of the Isotopes that are stable this is called the valley of stability and every other isotope is radioactive in one way or another. But why does the valley end after elements have more than 802 protons to explain this let's take a look at a stable nucleus and how its neutrons and protons interact with each other. There are two fundamental forces at play here the strong nuclear force and electrostatic repulsion. The strong nuclear force is a force that holds neutrons and protons together. Conversely electrostatic repulsion causes protons to repel one another. so his elements get heavier and heavier the number of protons will increase and this repulsion becomes larger and larger eventually out strengthening the formerly strong strong nuclear force and all Heavy elements eventually become unstable. At a certain point this repulsion will be so large that elements won't be able to form in the first place.


Island of stability
Island of stability

This isn't good for a hope of an infinite number of elements. To understand why let's take a look at the predicted half lives of isotopes with more than 82 protons. If we quickly draw an extension of the value of stability. We see that these elements are radioactive but have quite long half lives. But the further we move from this line the less and less stable these Isotopes become with shorter and shorter half lives. But if we zoom out a little bit further we find this the island of stability where a cluster of isotopes have uncharacteristically long half lives. But this doesn't quite answer the big question. How large can an element get?


There's a bit of a folk Legend amongst physicists that Richard Feynman wants to the back of the envelope calculation to show that any element with an atomic number of 137 or greater would have its lowest energy electron traveling faster than the speed of light. Which is impossible in reality if this folk legend is true at all, this was likely just a playful exercise rather than any proper science. In a more serious bit of science Feynman did confirm that elements above an atomic number of 137 might cause some issues.


Atomic equation

This slightly scary looking equation tells us the energy of an electron if we look at elements with more than 137 protons it turns out their energy would have a square root of a negative number in it. This is definitely breaking the rules a bit and is often a handy tool physicists use to prove the non-existence of something. But this also turned out to be a little bit of a simplification with modern calculations presenting the possibility of elements all the way up to an atomic number of 172. Since then a range of potential extensions to the periodic table have been presented. Each of which ending somewhere around 172 electrons.



However some theoretical physicists have gone a bit further than that and come up with a hypothesis called the continent of stability. The idea is that if nuclei get heavy enough, they would no longer Simply Be atoms with neutrons protons and electrons but rather the neutrons and protons are broken apart into up and down quarks. This would result in a kind of free flowing soup known as 'up down Quark matter' and could possibly only exist under the Colossal pressure of a supernova or the famously dense neutron star.


Whilst these aren't really elements anymore because they don't have neutrons protons and electrons they can keep increasing in Mass somewhat indefinitely and are even stable to certain types of radioactive decay. So maybe they'll be the key to finding heavier and heavier particles. So we don't know exactly but based on our current understanding of physics we know that the periodic table may end somewhere around an atomic number of 172 and the unobtainable probably is unobtainable but the continent of stability may be our route into understanding heavier and heavier matter. I hope you enjoyed reading this article and subscribe so you can get email notification whenever we post new article.


References:


[1] “The Technical Details: Radioactive Decay.” 2002. Global Monitoring Laboratory.


[2] Napy1kenobi. “Chart of the nuclides showing the ratio of protons to neutrons, with a black 'Island of Stability' in a 'Sea of Instability.”.


[3] Zagrebaev, V. 2016. “Opportunities for synthesis of new superheavy nuclei (What really can be done within the next few years).” 11th International Conference on Nucleus-Nucleus Collisions.


[4] Ball, Philip. 2010. “Column: The crucible | Opinion.” Column: The crucible | Opinion | Chemistry World.


[5] Scientific Opportunities with a Rare-Isotope Facility in the United States. j7st 2006. N.p.: National Research Council.


[6] “Unseptbium.” The Elements Wiki.


[7] Holdom, Bob. 2018. “Quark Matter May Not Be Strange.” Physical Review Letters.


[8] Holdom, Bob; Ren, Jing; Zhang, Chen. 2018. “.Quark Matter May Not Be Strange.” Physical

Review Letters.

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