The reason radioactive isotopes emit radiation is that the emission of radiation is a nutural consequence of being radioactive.Let's look a bit more closely. Radioactive isotopes are unstable atoms, and they will undergo radioactive decay sooner or later.The unstable atomic nuclei undergo a change based on what particular isotope is being considered. In any case, when a nuclear change occurs, radiation of some kind is emitted from that nucleus. radioactive isotope is a form of an element that is unstable and eventually decays into a different element. For example, most Carbon has 6 protons and 6 neutrons, and is st … able. This is called Carbon12.