Surely radioactivity is a natural phenomenon? There are two isotopes of helium, neither of which are radioactive.
An isotope is radioactive if its nucleus is "unstable". A highly unstable nucleus, such as Polonium-210, which was used to murder Alexander Litvinenko, has a very high Decay Constant and, consequently, a very short Half Life (a few weeks)
A slightly radioactive active isotope, such as Uranium-238, has a very low Decay Constant and a very long Half Life (over 4000 million years).
What is the Half Life of an isotope such as Carbon-12? It seems stable and has never been observed to decay. Does it have zero Decay Constant and therefore an infinite Half Life?