Although radioactivity is a common process happening all around us every day, it wasn't until the development of quantum mechanics that the process of radioactive decay was fully understood.
In alpha radioactivity consider the nucleus of say a Radium nucleus (88 protons and 138 neutrons) to consist of an alpha particle closely bound to the rest of the nucleus (86 protons and 136 neutrons). See Figure 2 below:
If we look at the potential energy diagram for the "bound" alpha particle, the combination of repulsive and attractive forces gives something like Figure 3 below:
The alpha particle starts out bound or "trapped" by the Radium nucleus. The energy of alpha is less that the peak repulsion energy, think about the wave function representation of the alpha particle in Figure 3. How does the alpha particle get out of the Radium nucleus? Explain you answer in terms of energy, wave functions and probabilities.