We need to start at the very beginning, looking at atoms. We know that these are made up of a nucleus, containing protons and neutrons, which is surrounded by electrons. Some elements can exist in several different forms called isotopes, which means that they have the same number of protons all the other forms, but a different number of neutrons.
Sometimes an isotope exists that isn’t very stable, a bit like your mad aunt who is always reinventing herself and finding a new life, and it wants to change, to get rid of some of its baggage and change into a more stable version of itself. This can be a neutron that leaves, or sometimes a proton, or perhaps even an electron. This is called radioactive decay and a little bit of radiation is also emitted by the atom when this happens.
Some isotopes are very unstable and so if you had a box full of them you might find that in a very short amount of time, lots of radiation had been emitted and that they were nearly all changed to the more stable version. On the other hand, some isotopes are pretty stable, and it might take a very long time for this to happen. We can measure this rate by the half life, which is the time it takes for the rate of emissions of radiation to drop by half.
So we can see from the graph that it takes the same amount of time every time for the radiation emissions to drop by half. This means that even if most of the particles decay very quickly, there will still be some very small amount of emissions for years to come. And in the case of particles which take longer to decay, the length of time over which they will emit their radioactivity can be very long indeed. This is at the heart of worries about radiaoactivity and nuclear power plants, because this radiation can be harmful and it’s important to stop it getting into water supplies or coming into contact with unsuspecting people for centuries.