[Music] hi and welcome back to sweet isolation cold UK by the end of this video you should be able to describe what's meant by the half-life of a radioactive isotope you should then be able to determine the half-life of a radioactive isotope and finally you should be able to calculate the decrease in radioactive count rate after a given number of half-lives that last statement applies only to higher-tier students over the last few videos we'd be looking at radioactive decay we saw that radioactive isotopes release radiation from the nucleus of their atoms remember that scientists cannot predict when a nucleus will decay and that's because decay is a random process in this video we're looking at the idea of half-life so let's get started the half-life of a radioactive isotope by the time it takes for the number of nuclei of the isotope in a sample to heart now that sounds a bit tricky but the actual idea is quite straightforward I'm showing you here a sample at a radioactive isotope the white circles represent the nuclei and when a nucleus decays I'm going to show that by turning it red so as you can see the nuclei are decaying remember that this is a random process sometimes as a relatively long period where no nucleus decays and other times several nuclei will decay in a short period so scientists cannot say when any individual nucleus will decay instead scientists determine the time it takes for half the original nuclei TDK and that's the half-life now this I could talk has a relatively long half-life we can tell that because it's decaying relatively slowly it will take a long time by the number of nuclei of the original isotope to have here's a different radioactive isotope and this one has a relatively short half-life we can tell that because the nuclei are decaying at a faster rate that means it won't take long for the number of nuclei of the original isotope to have now there is another definition for half-life which I'm showing you here the half-life is also the time it takes for the count rate or the activity from a sample containing the isotope to fall to half its initial level and as we saw before the count rate at the number of decays per second recorded by a detector such as a Geiger molar tube now you could be asked to work out the half-life of an isotope from a graph such as this one this shows how the number of undecayed nuclei remaining in a sample of isotope changes with time we're starting with 1,000 undecayed nuclei and we need to find the time it takes this to half half of one thousand is 500 looking at the graph we can see that it takes 20 minutes for the number of nuclei to fall from 1,000 to 500 so the hard life is 20 minutes after another 20 minutes we can feel that the number of undecayed nuclei has fallen by half again to 250 now you could also be asked to calculate the decrease in count rate after a given number of half-lives here the typical question a radioactive isotope has a half-life of 15 days and an initial count rate of 200 times per second determine the current rate after 45 days now remember that after each half-life the count rate will have halved the half-life is 15 days so 45 days is 3 half-lives that means that the count rate will have halved three times so the initial current rate is two hundred counts per second after 15 days it will evolve to 100 fifteen days after that it will have heart again 250 and finally 15 days later it will have halved again to 25 counts per second remember that you'll find plenty of questions on halflife in my vision workbook and you can get that by clicking on the link above okay so hopefully now you should be able to describe what's meant by the half-life of a radioactive isotope you should then be able to determine the half-life a radioactive isotope and finally you should be able to calculate the decrease in radioactive count rate after a given number of half-lives [Music]