### ChemTeam: Half-life problems involving carbon

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the This half life is a relatively small number, which means that carbon 14 dating is not We can use a formula for carbon 14 dating to find the answer. If the fossil has 35% of its carbon 14 still, then we can substitute values into our equation. Radioactive Dating and Half Life Name When doing calculations involving half- life, make a table listing the amount of Steps to solving half-life problems: what you're solving for (indicate what column in the table the answer will appear). HALF-LIFE PROBLEMS Name Block I. An isotope of cesium (cesium) lias a half-life of 30 years. f:^ UP i ^, ;5 "~ HALF-LIFE WORKSHEET Name Use Reference Table on side to assist you in answering the following questions. If a sample originally had atoms of carbon, how many atoms will remain after .

Understand the relative ages of layers from the law of superposition and what fossils are, but need not yet know exactly how the absolute ages of rock layers or fossils are determined. Have knowledge of the geologic time scale and the names of the eons throughout history.

Instructional Suggestions This lesson is intended to be completed in 1. The lesson plan indicated below is presented in time-oriented breakdown: Begin class with a brief introduction to the concept of radioactivity. If you do not have access to these, a class discussion, read aloud from an appropriate selection of textor other video review would be appropriate.

### Carbon 14 Dating - Math Central

Be sure to define the following words with the class: Discuss the possible uses of radioactive material in science. BBC Bitesize goes on to explain radioactive dating in the following sectionthough it is only text and images, without an interactive video. Introduce the MEA lesson concept: What happens over that 5, years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points.

So if you go back after a half-life, half of the atoms will now be nitrogen. So now you have, after one half-life-- So let's ignore this.

So we started with this. All 10 grams were carbon. This is after one half-life. And now we have five grams of c And we have five grams of nitrogen Let's think about what happens after another half-life. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon So let me actually copy and paste this one. This is what I started with. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here.

Let me clean it up a little bit.

## Radioactive Dating: Half-Life & Geologic Time

After one one half-life, what happens? Well I now am left with five grams of carbon And by the law of large numbers, half of them will have converted into nitrogen So we'll have even more conversion into nitrogen So now half of that five grams. So now we're only left with 2. 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. 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? 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. 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?

### Radioactive Dating: Half-Life & Geologic Time -

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. And this is just when you're doing it with a discreet you know, when you're right at the half-life point.