The radioactivity of an atom is dependent on

Radioactivity is the emission of ionizing radiation or particles caused by the spontaneous disintegration of atomic nuclei. Particles are emitted from the nuclei as a result of nuclear instability. 

The radioactivity of an atom is dependent on the difference in binding energy .
(comparing the before and after states, the binding energy of the product nucleus and the binding energy of the initial decaying nucleus)