# Stability of isotopes

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?

• 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. – Ben Crowell May 2 at 18:34