Question

When does the nucleus of an atom become radioactive?

Answer 1

When it has an atomic number higher than that of Lead (Pb) - it will become unstable and release Radiation.
OR
The nucleus of an atom becomes radioactivity when the number of neutron becomes more than the number of proton i.e. the neutron , proton ratio becomes more than 1.5
In such atoms the nucleus is unstable. to make the nucleus stable they undergo nuclear changes which is termed as radioactivity
Radioactivity is a phenomenon mainly shown by heavy metals and the isotopes of some light metals.