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If it can happen, it will

Subatomic particles do not behave like everyday objects. We can't really say what a particle will do, only what a particle might do. Particles move around like everyday objects and have momentum, but they also have wave properties. Quantum mechanics, the mathematical basis for our theories about particles, explains the behavior of particles in terms of probabilities.

Since particles are wave-like, it is impossible to know both their position and their momenta. While it is easier to think of particles as point-like spheres (which is how we have illustrated them throughout this site) this is misleading since they are better thought of as fuzzy regions in which you are most likely to find the particle.

Protons and neutrons migrate around inside a nucleus. There is a tiny, tiny chance that a conglomeration of two protons and two neutrons (which form an alpha particle) may, at the same instant, actually migrate outside the nucleus. There is a greater chance of this happening in a large nucleus than in a small one.

The alpha particle would then be free of the residual strong force trapping it inside the nucleus, and like a suddenly released spring, the charged alpha particle would fly away from the nucleus.

This idea that "if it can happen, it will happen!" is fundamental to quantum mechanics. For some atoms there is a certain probability that it will undergo radioactive decay due to the possibility that the nucleus may --for the shortest of instants-- exist in a state that allows it to blow apart. You cannot predict when a particular atom will decay, but you can determine the chance that it will decay in a certain period of time.