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Yesterday I was looking at the semi-empirical mass formula and calculating some binding energies of specific nuclei. Eventually I came across this website that listed both total binding energies per-nucleon and total binding energies of the nucleus.

To my surprise I found that for many, if not all elements that the binding energies for unstable isotopes was higher than the binding energies for stable. Take for example the page for Osmium where the first truly stable isotope is apparently tenth in binding energy per-nucleon.

I must be missing something. I thought that binding energy was the main factor in keeping a nucleus stable and that the most stable isotopes for every element would be have the highest binding energies respectively. What am I missing here?

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The binding energy of a nucleus is only sufficient to tell you whether that nucleus can spontaneously decay into separate nucleons. That type of decay is essentially nonexistent in practice. In reality we get things like alpha and beta decay. Then stability depends on the difference in mass-energy between the initial nucleus and the final nucleus or nuclei.

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  • $\begingroup$ I'm still not exactly following to be honest. Are you saying the larger the difference in mass-energy between parent and daughter nuclei, the more stable the nucleus? How exactly does this determine the stability of a nucleus in general? $\endgroup$ – ShroomZed May 2 at 17:17
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    $\begingroup$ For $\Delta M<0$, decay is possible. For $\Delta M>0$, it's not possible without an outside input of energy, i.e., spontaneous decay is impossible. It is also usually true that the rate of decay grows rapidly as $\Delta M$ becomes more negative. $\endgroup$ – Ben Crowell May 2 at 18:34

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