There are 80 stable elements in the periodic table. These elements have at least one stable isotope. Other elements don’t have any identified stable isotopes. The existence of stable isotopes can be easily verified by synthesizing the isotopes near the beta stability curve. If no stable isotopes are identified among them, it’s very unlikely for other isotopes to be stable.
However, some unstable isotopes can have very long-lived metastable high energy states known as isomers. The best known example is Ta-180m. Ta-180 decays into tungsten or hafnium in only a few hours, but its high energy isomer Ta-180m is so stable that no decay has been observed so far. However, the existence of long-lived isomers is much harder to rule out. Unlike isotopes, isomers are not uniquely defined by the proton and neutron numbers. Moreover, isomers can be stabilized by many different ways such as high nuclear spin, nuclear deformations and spin projection, which makes it difficult to exhaust all possibilities. It’s also very difficult to create some isomers artificially. So could there be other long-lived isomers, including isomers of radioactive elements like technetium and promethium which are not yet identified? Are there theories to predict their existence?
