Etydhv

Why do unstable nuclei form? Is it that we simply find unstable nuclei in nature and understand what these nuclei do in order to become more stable?

I feel like textbooks gloss over this question when addressing radioactivity.

There are a few different ways that unstable nuclei are produced:

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  Nuclear fusion is quite a common way to produce unstable nuclei in nature. At high enough energies, stable nuclei can fuse together to create unstable ones. For example, one step of one of the usual hydrogen-burning sequences in stars combines a helium-3 nucleus and a helium-4 nucleus (both of which are stable) into a beryllium-7 nucleus, which is unstable, with a half-life of roughly 53 days. Stars generally use nuclear fusion to produce most elements from boron up to roughly iron in their lifetimes. Nuclear fusion also plays a prominent role in the creation of even heavier elements, in more extreme conditions like supernovae, neutron star mergers, and other cataclysmic events. It's also how we produce many of the heavy synthetic elements in the laboratory, when we collide relativistic ion beams with a fixed target.


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  Neutron capture can also turn a stable nucleus into an unstable one. Since neutrons are uncharged, they are unaffected by the Coulomb repulsion of the protons of the nucleus and can incorporate themselves rather easily into even a stable nucleus at the right energy. Even common building materials like concrete and steel can become radioactive in the presence of enough neutron radiation at the right energy. Neutron capture can even induce nuclear fission, and in fact this is the mechanism by which nuclear fission reactors operate. Oftentimes these reactors are kickstarted using a "neutron gun" which injects neutrons of the right energy into the reactor core.


• 
  Decay of other unstable nuclei is a rather obvious one, but still needs to be included as it's a distinct process. Most of the nuclei we see on Earth with short half-lives are themselves the decay products of unstable nuclei with longer half-lives. For example, the radon gas that accumulates in basements is one of the decay products of uranium-238 that has been in the soil basically since the Earth was formed.


• 
  Neutrino interactions are a tiny, but notable, contribution to nucleosynthesis. A high-energy neutrino has a small, but nonzero, probability of knocking a proton or neutron out of a nucleus. In supernovae, there are an absolutely staggering amount of neutrinos produced (obligatory xkcd what-if: https://what-if.xkcd.com/73/); since there are so many high-energy neutrinos flying around, there are actually a non-negligible number of neutrino-induced nuclear reactions that happen, and it's currently believed that neutrino-induced nucleosynthesis partly explains the observed abundances of some light odd-numbered nuclei like fluorine-19.

This is not necessarily an exhaustive list, but you'll notice that it contains both examples found in nature and examples produced in the laboratory.

There's no fundamental principle that makes unstable states unable to exist. It's just that by being unstable, they won't exist for a long time. For example, take a cone. You could sit the cone on a table with its base at the bottom, and that would be stable ("stable" here means that if there is a small perturbation, the object settles back to its original state). You could also sit the cone on a table with its tip and the bottom, and that would be unstable. The unstable state won't remain for long - the slightest wind will cause the cone to topple over - but in principle, you can do it.

The same goes for unstable nuclei. You can make unstable nuclei - and they are made, in stars for example, or particle accelerators. You don't expect them to last very long, and many indeed do not (although there are also unstable nuclei that last for millions of years), but you can still make them.

Why make them? In stars, they're simply a consequence of the other things that are going on. In particle accelerators, it's because we want to make them for whatever reason.

Unstable nuclei form in many different ways. First of all, many are created in old stars, especially when they explode as supernovae. This is the case for all elements with atomic numbers higher than Iron, as they are not formed during the normal life of a star.

As a result, elements like $^238U$ with a half life of 4.5 billion years, were formed in supernovae and are older than the solar system. However $^235U$ has a half life of only 700 million years. Only about 1% of any $^235U$ formed before the solar system is still around. This problem is even worse with isotopes with even shorter half lives, e.g. $^14C$ which has a half life of only 5700 years.

Such isotopes are formed here on earth through various processes. For example, $^14C$ is created when particles (cosmic rays or solar particles) strike $^14N$ atoms