 Most of you have probably already heard the word half-life when describing radioactive decay. The concept of a half-life works because any measurable amount of atoms is generally a very large number, and this means that the probability of decay allows us to predict the number of total decays with some certainty. For example, imagine we have one gram of potassium-40. If you do the maths, this turns out to be a very large number of atoms. One gram times one mole per 40 grams times Avogadro's number of atoms per mole is equal to 1.51 times 10 to the 23 atoms. This is a very big number, 151 with 21 zeros after it. Now the half-life of potassium-40 is 1.251 billion years. The half-life means that if we wait for 1.251 billion years, half of the potassium-40 will have decayed. This is related to the fact that the probability of decay per unit time is constant. If we know this probability, then we can predict how long it will take for half of the nuclei to decay, and this length of time is the half-life. So after 1.251 billion years, the number of atoms left will be half that at the start, that is 0.755 times 10 to the 23 atoms. Now remember, even after all this time, the probability of decay remains the same. So after another 1.251 billion years, the number of atoms left will halve again. At this point, even though 3 quarters of the atoms have decayed, the number that are left is still a very large number. And the decay probability remains constant. So we can still predict with some certainty that after another half-life, the number of atoms will halve again. Following this logic, we can write the general relationship that after n half-lives, the number of nuclei that are left is equal to the original number of nuclei, n0, times 1.5 to the nth power. Let's now look at a different question. If the half-life is very long, surely the decay rate, that is the number of decays per unit time, will be low. However, this is not necessarily true. In fact, our 1 gram of potassium will exhibit 2.65 million decays per second. At first glance, this seems like a very large number of decays. But you have to remember that since Avogadro's number is so huge, 2.65 million decays per second is only the tiniest fraction of the total number of potassium-40 atoms that are present.