 My name is Kevin Conley. I'm an instructor at Foresight Tech, and I'd like to complete our lecture set on nuclear chemistry by going over with you the concept of half-life. Half-life includes a little bit more calculation than we've done in the past, and I'd also like to tell you conceptually what's going on. What's going on with half-life is, if you have a radioactive isotope, the number of decays that occur depends upon the amount of substance that you have. Every individual particle has a certain probability of decaying after a certain amount of time. So when you have a huge chunk, the chunk decays as a fraction of time. So what happens is you lose half of it after a certain period of time. So you go down to 50% after one half-life, 25% after two half-lives, and after a third half-life you go down to only 12.5% of the amount that there was originally in the sample. So that's the concept of half-life. An important application of half-life is the concept of radiological dating, and this has to do with the carbon-14, carbon-12 relative abundance on the earth. There is a relative abundance between these two where carbon-14 is a very small fraction of the carbon, which is why, well, it's a small fraction, parts per a million or something of that type. And also the C12 ratio on other planets and celestial bodies is different, which is why you can tell a moon rock or a Mars rock from something from the earth. But in any event, radiological dating has to do with this ratio. So if we take a look at a living organism such as a monkey eating a banana off a banana tree, as long as the monkey eats the bananas that are naturally occurring, the monkey and the tree, the reservoir of all this carbon will remain in a C14, C12 balance. So you can't really tell the age of the monkey. But if the monkey dies and turns into a skeleton or certain remains, is that right? Yes. Then what happens is no longer is the dead monkey in a balance with this carbon reservoir. The carbon-12 that was part of the monkey's body will remain, but the carbon-14 will begin to decay naturally. And as a result, the dead monkey will contain much less C14 than C12. By taking a look at the C14 to C12 ratio and knowing the half-life of C14, which is a few million years, you can then determine the age of the monkey's remains. Now let's take a look at a calculation. This is a calculation involving a given isotope. So how many grams of a 20-gram sample of Technetium 99 metastable remain after one day? The half-life of Technetium 99 M is 6.0 hours. This is a very interesting element because this is one element that does not occur naturally, and it's right in the middle of the periodic table. And Mendeleev and others predicted that this element would in fact exist. So the first step is to determine the number of half-lives that have in fact passed. So I start by writing down my piece of given information, which is one day. And I want to come up with a number of half-lives. This is time, so I want to end up with an amount of time. So if I have one day, and I convert the day to hours, 24 hours over a day, and then I convert the hours to number of half-lives, I go day and day cancel, hour and hour cancel, and the only unit that remains is half-life. So I have 24 divided by 6 will give me four half-lives passed during every day. The second step is to determine the amount of radioisotope remaining by dividing the original amount by two for each half-life. You see we divide by two for the first half-life, another two for the second, and another two for the third, and so forth. In this case, we have a fourth half-life. We divide by two again. So we begin with 20 grams, divide by, for each half-life, one, two, three, and four times. So we have 20, 10, five, two and a half, and finally, 1.25 grams of metastable technician 99 remaining. That's it. Bye-bye.