We've already discussed the stability of nuclei and that it came modes that allow an unstable nucleus to eventually evolve through the emission of alpha beta and gamma radiation to end up as a stable nucleus. However, you might have some questions such as how long do these processes take? What is the time scale for the nucleotok of unstable nuclei? The answers to these questions lead us to the concept of a nuclear half-life and that is the subject of this video. Let's do a thought experiment. I mentioned in the last lecture that the massive ecalcium-forting nucleus was less than that of potassium-forty and I described how potassium-forty can be to decay into calcium-forty. So we said that this process can happen but here is the interesting question, when will it happen? To be more precise, if we have a single atom of potassium-forty, can we say exactly when it will decay to calcium-forty? The surprising answer turns out to be that no, we can't say when it will decay. In fact, it turns out that the only thing we can know is the probability that the nucleus will decay in a given time interval. What does this mean? It means that if we watch a potassium-forty nucleus for some time interval, let's say a hundred seconds, we can know the exact probability that it will decay during this time. Let's call this probability X percent. But let's say that this particular potassium-forty nucleus doesn't decay in that first 100 seconds. Passory walk away and we come back an hour later and it still hasn't decayed. Here we have to deal with something really interesting and somewhat counterintuitive. The probability of that potassium-forty nucleus decaying in the next 100 seconds is exactly the same as it was in that first 100 seconds over an hour ago. This might seem really weird the first time you think about it, but the fact is that the past history of the atom is irrelevant. In any new observations of a potassium-forty atom, the probability of decay per unit time is constant and I'm changing. This constant probability leads us to the following observation. For a large number of nuclei, we can predict with some accuracy how many decays will happen in a given time. However, for any one nucleus, the exact time of its decay is inherently probabilistic and cannot be predicted with any certainty.