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About this Lesson
 Type: Video Tutorial
 Length: 10:30
 Media: Video/mp4
 Use: Watch Online & Download
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 Posted: 07/14/2009
This lesson is part of the following series:
Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Nuclear Chemistry (8 lessons, $12.87)
Chemistry: Rates of Disintegration (2 lessons, $3.96)
This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidationreduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.
Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electronrich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.
Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies moleculebased magnetism.
Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.
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Archeologists and anthropologists use radioactivity in an interesting way in order to figure out how old the objects are that they have discovered. And on technique is called radiocarbon dating, and it relies on carbon 14. Now, carbon 12 and carbon 13 are the usual isotopes of carbon  they're both stable. But carbon 14 is radioactive. And it is formed high up in the atmosphere in a reaction in which nitrogen 14 reacts with a neutron. The neutron just comes from outer space. Again, we are constantly being bombarded by radiation. And with the reaction of a nitrogen 14 with a neutron, we can make a carbon 14 and a proton, and proton decay is something that we haven't really talked about. It's not really important so we won't get into it any more than that. But in any case, what happens is, a nitrogen 14 gets converted into a carbon 14. Now the carbon 14 is also, simultaneously, decaying by a beta elimination, in which carbon 14 goes back to a nitrogen 14. And both these processes are going on at the same time, and so there is a steady state concentration of carbon 14 in the environment. In much the same way as if you have a bathtub and you pull the stopper in the bathtub and the water starts to drain out, but you turn the water on and start filing the bathtub at the same time, then you will have a steady state level of water in the bathtub, we have a steady state concentration of carbon 14 in the environment, even though its radioactive.
Now, we have to make an assumption, and the assumption is that the level of carbon 14 hasn't changed over the last 50,000 years. And what I'll show you is that carbon 14 dating is only good for less than 50,000 years. The reality is, that's probably a reasonable assumption because things just don't change. Nuclear processes that would give rise to the carbon 14 probably haven't been affected on that time scale.
Now, carbon 14 decays with a halflife of 5,730 years, and that turns out to limit the range over which we can use radiocarbon dating, because we have to have some carbon 14 that's detectible in the sample in order to determine how old it is. And I told you before that after 10 halflives, the amount of stuff that you have left, which is 2^10 or or about of what you started with. That becomes experimentally limiting. You just can't measure such a small amount. So something on the order of 40,000 years is the oldest thing that we can date by radiocarbon dating. So how does radiocarbon dating work?
The idea is that carbon 14 that is created in this reaction of nitrogen with a neutron is incorporated into the environment in the form of, say, CO[2] or anything else that contains carbon, and ultimately gets incorporated into plants. And then the plants get eaten by cows. And then the cows get eaten by people. Or it's incorporated into the cotton, which is a plant. And then someone takes the piece of cotton and they weave it into a piece of cloth. In any case, so long as an object is alive  so long as it continuously exchanging carbon dioxide with the environment  either via plant matter or by breathing  it is going to have the equilibrium level of radioactivity due to carbon 14. And that radioactivity is reported in specific activity units, which is disintegrations per gram of carbon. And it turns out that that number is about 15.3 disintegrations per minute per gram of carbon.
Now, the assumption is that that hasn't changed, that the specific activity doesn't change. But that makes sense, because the specific activity is a kinetic phenomenon and we don't expect that carbon 14 decays at any rate that's different from what it did 50,000 years ago. So that assumption is not too bad.
So something that's alive is going to have some amount of carbon 14, which gives rise to 15.3 disintegrations per minute per gram. But once that thing dies  one that thing is no longer part of a living plant  then the carbon 14 concentration is going to start to go down as a result of the decay. In other words, it isn't going to be continuously replenished, because it isn't part of the environment anymore. And so, as soon as the cotton is picked and woven into a cloth, the clock sort of starts. And at that point, the carbon 14 concentration is going to start decreasing. Or when somebody dies, the carbon 14 concentration is going to start going down.
If somebody tells you that they dated a pottery shard of a piece of a pot by carbon 14, don't believe it, because an object has to have been alive in order to exchange carbon 14 with the environment in order to correctly date the object. But you can date a tree that way. You can date a piece of cloth. You could date a mummy.
So here's an example  a piece of linen, with a specific activity of 11 decays per minute per gram due to carbon 14, is discovered. Approximately how old is that piece of cloth? And we already have talked about the fact that we can relate the number of carbon 14 nuclei today to the number that were originally there by the firstorder rate constant the time that's gone by since we started measuring. And we also said that this equation also applies to activity  which is  and then we also consider that it applies to specific activity, because that would just have units of disintegrations per gram over disintegrations per gram. Again, a dimensionless unit.
Well, this expression  . That's using the equation that K = ln2 divided by the halflife. And we can rearrange this equation to solve for T  the amount of time that's gone by, and it's just equal to minus the halflife divided by the natural log of 2 times the natural log of the activity over the equilibrium activity  the activity when the thing is alive. So the activity is dropping as the thing gets older and older.
So we plug in our values. The piece of linen now has a specific activity of 11 disintegrations per minute per gram. If it's alive, it would be 15.3 disintegrations per minute per gram. And plugging in all of our other constants, including the halflife of carbon 14, and we get that the object is 2700 years old. Okay? Simple enough. That's how carbon 14 dating works. But remember that you can only date with carbon 14 things that were once alive. And so suppose you wanted to date a rock. If you wanted to date a rock, what you'd have to do is find some other way to decide how old the rock is. Carbon 14 is not going to help you. And what can help you, if the rock contains Uranium 238, is that we can consider how much uranium 238 there is today. And if we knew how much there was originally in the rock, we could figure out how old the rock is. Well how can we figure out how much uranium 238 there was originally, and the answer is, Uranium 238 decay is by a series of steps that we've already talked about, ultimately to lead 206. And lead 206 is not the most common isotope of lead. And so it's an unusual isotope of lead, and we can measure how much of this unusual isotope there is, and assume that it all came from the uranium 238. So we have a rock, and when it's born  when it coalesced  it had only uranium 238 and no lead 206. And then, as it lives its life, the uranium 238 concentration decreases, or the number of nuclei of uranium 238 decreases. And as that goes down, it makes lead 206. Well we can relate how much lead and how much uranium there is to knowing how much uranium there was originally.
Suppose that our rock contains .257 milligrams of lead 206 for every milligram of that's in our rock. Then we can backcalculate how much uranium 238 there was originally. Suppose that there is now 1.000 milligrams. Well, that means the original had that amount plus the amount that has since become lead. And if you think about the stoichiometry, you get one lead for every uranium. So if we have .257 milligrams of lead now for every 1 milligram of uranium, then original amount of uranium that gave rise to this amount of lead is just 238 grams per mole divided by 206 grams per mole times the mass of the lead that's present. And so we add these two quantities, and it says that when the rock was born, the uranium, which is now 1 gram, represented 1.297 milligrams. See now that it's 1 milligrams, when it was born, it was 1.297 milligrams. Okay?
So now, we can convert that to numbers of nuclei of uranium. While recognizing that mass is directly proportional to the number of nuclei for a pure compound, we can just use directly the where instead of N being the number of nuclei, N is going to be the mass of the sample of uranium now versus the mass of the uranium originally, and it's still equal to negative the firstorder rate constant times how much time has gone by. We can rearrange this to solve in terms of T, the time, and we need to know what K is but we can get that from the halflife. So the firstorder rate constant is 1.5 x 10^10 inverse years for uranium 238. And that's using the halflife of uranium 238. And then we can solve this by plugging in for K, the firstorder rate constant, the mass of uranium in the sample of today, the mass that was there when the rock was born and we work all this out and we see that 1.7 x 10^9 or 1.7 billion years have gone by since the rock was born.
So I've showed you a couple of methods by which archeologists and anthropologists and geologists can date things that takes advantage of radioactivity and the fact that it's a firstorder process. And if we know the halflife, we can calculate how old an object is if we know how much there was originally and how much there is now  that's in the case of uranium  or how much there ought to be if the object is exchanging carbon 14 with the environment versus how much it has now that's been dead for awhile.^
Nuclear Chemistry
Stability of Atomic Nuclei and Rates of Disintegration
Radiochemical Dating Page [2 of 2]
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