And how much nitrogen?

Well we have another two and a half went to nitrogen. So now we have seven and a half grams of nitrogen And we could keep going further into the future, and after every half-life, 5, years, we will have half of the carbon that we started. But we'll always have an infinitesimal amount of carbon. But let me ask you a question.

Let's say I'm just staring at one carbon atom.

## ChemTeam: Half-life problems involving carbon

Let's say I just have this one carbon atom. You know, I've got its nucleus, with its c So it's got its six protons. It's got its eight neutrons. It's got its six electrons. What's going to happen?

## Half-life and carbon dating

What's going to happen after one second? Well, I don't know. It'll probably still be carbon, but there's some probability that after one second it will have already turned into nitrogen What's going to happen after one billion years? Well, after one billion years I'll say, well you know, it'll probably have turned into nitrogen at that point, but I'm not sure. This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon So after one half-life, if you're just looking at one atom after 5, years, you don't know whether this turned into a nitrogen or not.

Now, if you look at it over a huge number of atoms. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. I don't know which half, but half of them will turn into it.

So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, and it has a half-life of two years. I'm just making up this compound.

### More Topics

And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left. And we want to know how much time has passed by. So 10 grams left of x. How much time, you know, x is decaying the whole time, how much time has passed? Well let's think about it. We're starting at time, 0 with 80 grams. After two years, how much are we going to have left? We're going to have 40 grams. So t equals 2. But after two more years, how many are we going to have?

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- Half-life and carbon dating (video) | Nuclei | Khan Academy?
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- Radioactive Half-Life Formula.

We're going to have 20 grams. So this is t equals 3 I'm sorry, this is t equals 4 years. And then after two more years, I'll only have half of that left again. So now I'm only going to have 10 grams left. And that's where I am. And this is t equals 6. So if you know you have some compound. You're starting off with 80 grams. You know it has a two-year half-life. You get in a time machine. And then you didn't build your time machine well. You don't know how well it calibrates against time. You just look at your sample. You say, oh, I only have 10 grams left.

You know that 1, 2, 3 half-lives have gone by. And you could also think about it this way. And that's what we have here. The quantity of radioactive nuclei at any given time will decrease to half as much in one half-life. Remember, the half-life is the time it takes for half of your sample, no matter how much you have, to remain. The only difference is the length of time it takes for half of a sample to decay.

Understand how decay and half life work to enable radiometric dating. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object. There are two types of half-life problems we will perform. One format involves calculating a mass amount of the original isotope. Using the equation below, we can determine how much of the original isotope remains after a certain interval of time. The half-life of this isotope is 10 days. For example, carbon has a half-life of 5, years and is used to measure the age of organic material.

The ratio of carbon to carbon in living things remains constant while the organism is alive because fresh carbon is entering the organism whenever it consumes nutrients. When the organism dies, this consumption stops, and no new carbon is added to the organism. As time goes by, the ratio of carbon to carbon in the organism gradually declines, because carbon radioactively decays while carbon is stable.

Analysis of this ratio allows archaeologists to estimate the age of organisms that were alive many thousands of years ago. Along with stable carbon, radioactive carbon is taken in by plants and animals, and remains at a constant level within them while they are alive. After death, the C decays and the C C ratio in the remains decreases.

Comparing this ratio to the C C ratio in living organisms allows us to determine how long ago the organism lived and died. C dating does have limitations. For example, a sample can be C dating if it is approximately to 50, years old. Before or after this range, there is too little of the isotope to be detected. Substances must have obtained C from the atmosphere. For this reason, aquatic samples cannot be effectively C dated. Lastly, accuracy of C dating has been affected by atmosphere nuclear weapons testing.

Fission bombs ignite to produce more C artificially. This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50, years ago. After 5, years, the amount of carbon 14 left in the body is half of the original amount. If the amount of carbon 14 is halved every 5, years, it will not take very long to reach an amount that is too small to analyze. When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is —0.

How old is the fossil? We can use a formula for carbon 14 dating to find the answer.