Hi, I'm Peter Edwards from Bluetutors. We teach children of all ages, right from primary school to degree level, and we find the highest quality tutors. Today, I'm going to teach you some maths. Now, we're going to look at how to calculate a half-life of something. The half-life simply means if we have a number of things, how long will it take before half of those are dead. We say “dead,” but it can mean a number of different things, as we will show an example in a second. So let's say we had ten carbon-14 atoms. These carbon-14 atoms are going to decay. They're going to decay over a period of time and they're going to change into carbon-12 atoms. So in any substance, you will have a number of Carbon 14 atoms and over time, these will slowly decay and we'll have more carbon-12 atoms. You also have carbon-12 atoms right from the start. It's a way of working out how long something has been dead for. So, the example I gave before, if we have ten Carbon 14 atoms in a particular substance and after a year we only have five, then the half-life of that substance would be said to be a year, because in that year, we've reduced the carbon-14 atoms by a half, from ten to five. So if we look at the example here, we have a number of carbon-14 atoms on the y-axis and time on the x-axis. Let's assume that we start with one hundred carbon-14 atoms, we'll say the time is T equals to one. So to calculate the half-life, what we have to do is find the time when there are only fifty carbon-14 atoms. That's going to be around here, and let's say the time here is T equals to ten. So that means we would have a half-life of nine. Ten minus one is nine, and that's how long it's taken for half of the atoms to decay. So if we were to have a point here, where T equals nineteen, which is another half-life, then we can come across here and this amount is going to be twenty five atoms. So the point of the half-life is that it's the number of the amount of time for half the atoms to decay. You can see that we end up with a graph like this which gets closer and closer to zero, but theoretically will never reach zero. That's how to calculate the half-life of a substance. .

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