# Half life dating equation

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Another approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value.This period of time is called the half-life of the reaction, written as . I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting. And it does that by releasing an electron, which is also call a beta particle. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? So that after 5,740 years, the half-life of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. But we'll always have an infinitesimal amount of carbon. Let's say I'm just staring at one carbon atom. You know, I've got its nucleus, with its c-14. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. After two years, how much are we going to have left? And then after two more years, I'll only have half of that left again. And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic. So one of the neutrons must have turned into a proton and that is what happened. And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen. And over 5,740 years, you determine that there's a 50% chance that any one of these carbon atoms will turn into a nitrogen atom. And we could keep going further into the future, and after every half-life, 5,740 years, we will have half of the carbon that we started. Now, if you look at it over a huge number of atoms. But after two more years, how many are we going to have? So this is t equals 3 I'm sorry, this is t equals 4 years. 1/2 to the 3rd power, because every time you have 1/2 of the original sample-- that's the number of half-lives-- after three half-lives you'll have 1/8 of your original sample. In the next video we're going to explore what if I asked you a question, how many of the particles, or how many grams will you have in exactly 10 days? And this is just when you're doing it with a discreet you know, when you're right at the half-life point. The rate of radioactive decay is an intrinsic property of each radioactive isotope that is independent of the chemical and physical form of the radioactive isotope. In this section, we will describe radioactive decay rates and how half-lives can be used to monitor radioactive decay processes.

The half-lives of several isotopes are listed in In our earlier discussion, we used the half-life of a first-order reaction to calculate how long the reaction had been occurring.Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.The techniques that have been developed for this application are known as radioisotope dating techniques.If two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life.The half-life of a first-order reaction under a given set of reaction conditions is a constant.