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Tellurium-128 is the longest lived radioisotope so far with a half-life of 2.3 septillion ($2.3*10^{24}$) years. I know I've heard something about so called "magic numbers" that if you have the perfect amount of protons and neutrons in an atomic nucleus it usually is radioactive but has an absurdly long half-life (examples bismuth-209,xenon-124). But why is tellurium-128 this stable? And why is this for the ones I have just said?

Wikipedia Link: https://en.wikipedia.org/wiki/Isotopes_of_tellurium

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Tellurium-128 is in no way extraordinary or unique.

Cape Chelyuskin in Russia is the northernmost extreme point of continental Eurasia. Tellurium-128 is not an extreme point of anything. There are hundreds of isotopes which are less stable than it and hundreds of those which are more stable. The latter kind is called simply "stable".

Now you might think there is a clearcut boundary between the stable isotopes and the radioisotopes. No, there is none. As our detection methods improve, more and more isotopes previously thought to be stable are found to have some decay path, usually with an absurdly long half-life (otherwise they would have been found earlier). When I was a kid, the heaviest stable element had the number 83. This is no longer the case.

Magic numbers of protons and neutrons have no role in this. Well, I mean, they are related to the same field: if a nucleus has either of these, or better both, it is expected to be more stable than its peers. $\rm^{128}Te$ doesn't and isn't.

If anything, $\rm^{128}Te$ is (or was; I didn't check) a temporary winner in a perpetual race. In due time, longer half-lifes will be detected, and then longer yet, and so on.

So it goes.

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