The nucleus of an atom exhibits radioactivity as a result of nuclear instability. Radiation released from an atom's unstable nucleus causes energy to be lost. The nucleus is held together by two forces: an electrical force of repulsion and the nucleus' tremendous forces of attraction. In the natural world, these two forces are thought to be immensely powerful. Because the mass of the nucleus gets quite large when condensed, the chances of meeting instability increase as the size of the nucleus grows. That is why Plutonium and Uranium atoms are exceedingly unstable and undergo the phenomena of radioactivity.
By chance, Henry Becquerel discovered radioactivity. In a drawer housing photographic plates, a Uranium compound was wrapped and deposited.