Two other characteristics of lead isotope measurements make it superior to other methods. First, measuring the isotope ratio of a single element can be done much more precisely than measuring isotope ratios of two differing elements. Second, using two isotopes of the same element makes the sample immune to chemical fractionation during a post-crystallization disturbance Dalrymple The commonly accepted 4. This model, which describes the accumulation of lead isotopes in meteorites, the Earth, and the Solar System, was proposed independently by E.
Gerling, Arthur Holmes, and Fritz G. Houtermans in the s Dalrymple This model ultimately led to the development of isochrons, in which two isotopes are plotted against each other to calculate an age for the mineral or rock.
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Those who developed the method utilized Pb and Pb, lead isotopes that are the product of radioactive decay, normalized to Pb. The amount of Pb will remain constant throughout the history of a rock because it is a stable isotope that is not the product of any decay series, thus allowing for the normalization Dalrymple Two requirements of the Gerling-Holmes-Houtermans model make it difficult to use.
The first is that it requires single-stage leads, which are systems that begin at some initial lead composition and remain on the same growth curve throughout their histories Dalrymple The second requirement is that assumptions about the genetic relationship between the Earth and meteorites must be made.
Although single-stage leads are difficult to find on Earth due to the constant recycling of Earth's crust, Pb-Pb isochrons remain powerful tools in making age of the Earth calculations. A Pb-Pb isochron plots Pb, the daughter isotope of U, versus Pb, the daughter isotope of U, with both normalized to Pb. The resulting line drawn through the plotted points will pass through a point representing the initial lead composition of the system.
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Although this point cannot be determined, the isochron will rotate about it as the rock ages because the initial amount of lead is constant regardless of age. An example isochron from Dalrymple is shown in Figure 4.
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The slope of the line gives the age of the rock. Unlike other isochrons, the slope of the Pb-Pb isochron decreases with increasing age. This is because U has a half-life of million years, while U has a half-life of 4. The rate at which daughter isotopes accumulate is dependent on the amount of parent isotope present.
Since U has a much shorter half-life, a larger fraction of the initial U present in the rock will have decayed compared to U. Therefore, Pb will accumulate at a slower rate than Pb, causing the isochron to decrease in slope with increasing age. The use of lead isotope ratios makes this isochron self-checking. A large scattering of measurements would indicate the sample is multi-stage rather than single-stage, making the isochron unreliable.
Another situation in which single-stage systems give unreliable information is the extraction of lead from uranium to form lead ore. It is possible that a system could undergo a geological process that extracts lead, leaving the new system without any uranium. If that system were dated at that point in time, it would fall on the isochron and give the correct age of the mineral. However, without any uranium present, accumulation of daughter isotopes ceases even though time continues to pass.
Such events produce a frozen record, giving the amount of time from crystallization to extraction of lead to form lead ore. Such ages are very useful because they can measure time forward from some known event in the past, such as the formation of the earth. The difficulties with single-stage systems can be circumnavigated with multi-stage systems.
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Though multi-stage lead samples cannot be used for generating isochrons, they can be used to produce valuable information through concordia-discordia plots. And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities. So let me write this down. And let me be very clear. Let's look at the periodic table over here. So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon So carbon is the most common.
So most of the carbon in your body is carbon But what's interesting is that a small fraction of carbon forms, and then this carbon can then also combine with oxygen to form carbon dioxide. And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. It can be fixed by plants.
When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue.
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And so this carbon, it's constantly being formed. It makes its way into oceans-- it's already in the air, but it completely mixes through the whole atmosphere-- and the air.
And then it makes its way into plants. And plants are really just made out of that fixed carbon, that carbon that was taken in gaseous form and put into, I guess you could say, into kind of a solid form, put it into a living form. That's what wood pretty much is. It gets put into plants, and then it gets put into the things that eat the plants. So that could be us. Now why is this even interesting? I've just explained a mechanism where some of our body, even though carbon is the most common isotope, some of our body, while we're living, gets made up of this carbon thing.
Well, the interesting thing is the only time you can take in this carbon is while you're alive, while you're eating new things. Because as soon as you die and you get buried under the ground, there's no way for the carbon to become part of your tissue anymore because you're not eating anything with new carbon And what's interesting here is once you die, you're not going to get any new carbon And that carbon that you did have at you're death is going to decay via beta decay-- and we learned about this-- back into nitrogen So kind of this process reverses.
So it'll decay back into nitrogen, and in beta decay you emit an electron and an electron anti-neutrino.
I won't go into the details of that. But essentially what you have happening here is you have one of the neutrons is turning into a proton and emitting this stuff in the process. Now why is this interesting? So I just said while you're living you have kind of straight-up carbon And carbon is constantly doing this decay thing. But what's interesting is as soon as you die and you're not ingesting anymore plants, or breathing from the atmosphere if you are a plant, or fixing from the atmosphere. And this even applies to plants.
Once a plant dies, it's no longer taking in carbon dioxide from the atmosphere and turning it into new tissue.
The carbon in that tissue gets frozen. And this carbon does this decay at a specific rate. And then you can use that rate to actually determine how long ago that thing must've died. So the rate at which this happens, so the rate of carbon decay, is essentially half disappears, half gone, in roughly 5, years. And this is actually called a half life. And we talk about in other videos. This is called a half life.
And I want to be clear here. You don't know which half of it's gone. It's a probabilistic thing. You can't just say all the carbon's on the left are going to decay and all the carbon's on the right aren't going to decay in that 5, years. So over the course of 5, years, roughly half of them will have decayed. Now why is that interesting?go to site
Well, if you know that all living things have a certain proportion of carbon in their tissue, as kind of part of what makes them up, and then if you were to find some bone-- let's just say find some bone right here that you dig it up on some type of archaeology dig. And you say, hey, that bone has one half the carbon of all the living things that you see right now. It would be a pretty reasonable estimate to say, well, that thing must be 5, years old. Even better, maybe you dig a little deeper, and you find another bone.
Maybe a couple of feet even deeper.
So how old is this? And then after another half life, half of that also turns into a nitrogen And so this would involve two half lives, which is the same thing as 2 times 5, years.
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