in today's video we're going to look at the terms activity and half-life and see how we can calculate each of them we've already seen that some materials contain unstable isotopes and that in order to become more stable they can decay by emitting some form of radiation like an alpha particle a piece of particle or gamma rays we call materials like this radioactive and they come in loads of different forms if we were to consider a single radioactive isotope we'd have absolutely no way of knowing when it would decay because the decay process is completely random however if we have a large enough sample of radioactive isotopes then even though we couldn't tell when any individual isotope would decay we can still find out two very useful things one is the activity of the sample which is the overall rate of decay of all the isotopes in our sample and we measure activity in becquerels where one becquerel represents one decay per second so if a sample had an activity of 600 macros then there must be 600 isotopes decaying each second in that sample the other important term to know is half-life which has two definitions and can be defined either as the time taken for the number of radioactive nuclei in a sample to half for example to drop from a million unstable nuclei to only 500 000 or the time taken for the number of decays so the activity to half for example to drop from 600 decays per second to 300 decays per second to properly understand these concepts let's imagine our radioactive sample as 100 unstable isotopes each of which can decay by emitting radiation in order to become stable so if we watch this sample decay the first thing we notice is that the decay process is completely random so we have no way of knowing when any particular particle will decay as time goes on though and more and more of them decay the number of unstable particles remaining decreases because there are fewer particles left to decay this means that the overall rate of decay which remember is activity will also decrease which is why it looks like the sample is decaying more slowly than it was at the start this is why we can define half-life as a halving of either the number of radioactive nuclei remaining or a halving of the activity they are both perfectly correlated because fewer radioactive nuclei means a lower activity another way to show this decay process is by using a graph that plots activity in becquerels against time as time goes on the number of particles remaining and the activity of the sample will decline but the rate of decline will also fall which is why it's curved rather than a straight line to calculate the half-life from a graph like this we need to find the time it takes for the activity to half so in this case drop from 600 to 300 which we can see is about two hours and to confirm this we could check another one by saying how long it takes it to half again down to 150 and indeed it does take another two hours so we can be confident that the half-life is two hours if we had a different radioactive sample though like this one we can see it is decaying much more quickly this means that it started with a much higher activity as we can see on our graph and also that it will decline much more rapidly and so a much shorter half-life this time of one hour now so far we've just kind of assumed that we're to know what the activity is in real life though we'd have to find the activity using a device called a geiger muller tube encounter these things record all the decays that reach them each second so all of those alpha and beta particles and gamma rays which it then records as the count rate and it says count rate that we use to estimate the activity before we finish let's try one quick question the half-life of a radioactive source is 40 hours there are initially 3 million radioactive nuclei in the sample how many nuclei will remain after five days in a question like this the idea is to first find out how many half-lives there'll be and then half the number of radioactive nuclei that many times so first we need to take five days and times it by 24 hours to get 120 hours and we can then divide that by 40 which is the source's half-life to find out that the sample would have undergone three half-lives so then we just take our three million radioactive nuclei and half them three times to get 1.5 million 750 000 and finally 375 000 which would be our final answer that's all for this video so hope you enjoyed it and i'll see you soon