A stable element by definition is a chemical element (found on the Periodic Table) that has atleast one stable, naturally occurring isotope. For example, Helium has 9 isotopes, but since two of them are stable (He-3 and He-4), Helium is considered to be a stable element.
Thereof, what makes an element stable or unstable?
The nucleus of this kind of atom is said to be stable. In some atoms the binding energy is not strong enough to hold the nucleus together, and the nuclei of these atoms are said to be unstable. Unstable atoms will lose neutrons and protons as they attempt to become stable.
Which elements are unstable?
Stable elements are those which have atleast one isotope with no tendency to “decay”, i.e., change into another element. They may have naturally-occurring unstable isotopes, such as Carbon (common C-12 is stable, natural C-14 is unstable). Unstable elements are those which have only unstable isotopes, such as Uranium.