This item is one of a special case - Known Unknowables
Radioactive decay is the process by which the nucleus of an unstable atom loses energy by emitting 'radiation' - which can be in the form of alpha particles, beta particles, gamma rays or conversion electrons.
The emissions are random in the sense that the exact moment that an alpha particle (for example) is emitted cannot be predicted. Neither can its direction of travel. This randomness is an integral part of current quantum theory, and is consistently confirmed by observations. That's to say that no-one can (or ever will be able to) predict when the next decay event will occur.
“According to the current model of quantum physics, it's completely and genuinely random.”
Source: Marcus du Sautoy, What We Cannot Know: Explorations at the Edge of Knowledge
Also see: Radioactive decay neutrino anomaly