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Author Topic:   Introduction To Geology
Dr Adequate
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Message 226 of 292 (684471)
12-17-2012 4:28 PM
Reply to: Message 225 by RAZD
12-17-2012 3:41 PM


Re: U-Pb, Pb-Pb, And Fission Track Dating
It should ... I knew I'd screw up one of those superscripts eventually. 'Twas but a matter of time.

Thank you.


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JonF
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Message 227 of 292 (684514)
12-17-2012 5:46 PM
Reply to: Message 224 by Dr Adequate
12-17-2012 3:17 PM


Re: U-Pb, Pb-Pb, And Fission Track Dating
Does the math of the Pb-Pb isochron require that we know the initial Pb-Pb ratio of the solar system?

Yup. Or something equivalent. The X and Y intercepts of the Pb-Pb isochron are meaningless. "Standard" isochrons start at the initial parent / nonradiogenic daughter point on the Y axis and can be considered to start there or be "anchored" there, since that point doesn't change over time. The Pb-Pb isochron is anchored at a point that is initially unknown and cannot be extracted from samples of one rock or lava flow or whatever. That point is the primordial lead ratios of whatever the sample came from, and the isochron forms a straight line only if the items sampled align with the line between that point and modern lead ratios (which are difficult to sample averaged across the entire Earth). Dalrymple devotes his entire last chapter to it, so it's obviously difficult to condense to a portion of a message.

The Canyon Diablo meteorite (AKA Meteor Crater AKA Barringer Crater) has so little uranium and thorium in it today that it cannot have had any significant amount of uranium and thorium 4.5 Bya, and therefore its lead ratios today are primordial for the Solar system and are the anchor point for that Pb-Pb isochron. Since then similar meteorites have been found. The achievement of Patterson's classic paper of 1956, Age of meteorites and the earth, which established the currently accepted age of the Earth, was to produce an independent and believable tie between meteoric lead and terrestrial lead.

Stassen has some interesting stuff at http://www.talkorigins.org/origins/feedback/may03.html, about a quarter of the way down the page (search for isochron).

The math of how the points come to lie along the Pb-Pb isochron is considerably more complex than the "standard" isochron, because the points "move" on the graph over time in a significantly more complex manner. Points representing individual samples on a "standard" isochorn "move" over time in straight lines, as illustrated at http://www.talkorigins.org/...n-dating/AnimatedIsochron.html. Points on the Pb-Pb diagram "move" along growth curves, two of which are shown in the figure above.

Edited by JonF, : No reason given.

Edited by JonF, : No reason given.

Edited by JonF, : No reason given.


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Dr Adequate
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Posts: 15485
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Message 228 of 292 (684523)
12-17-2012 6:16 PM
Reply to: Message 227 by JonF
12-17-2012 5:46 PM


Re: U-Pb, Pb-Pb, And Fission Track Dating
Ah, I see. My sources weren't really clear on that point, but I've found some which are.

Thanks for taking the time to put me straight. I shall add something about anchoring.

As for the growth curves, I don't think I need to go into that much detail, but maybe I should say that the data points will lie on a straight line as with an ordinary isochron, but for different reasons. The important idea I want to get across is that we do have several data points and that they do have to agree by lying on an isochron. The actual math behind it would, I think, fall under "further reading" for those readers who are willing to pursue it and capable of doing so.


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JonF
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Message 229 of 292 (684524)
12-17-2012 6:21 PM
Reply to: Message 228 by Dr Adequate
12-17-2012 6:16 PM


Re: U-Pb, Pb-Pb, And Fission Track Dating
Yeah, I like that. It's accurate and informative.
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Dr Adequate
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Posts: 15485
Joined: 07-20-2006
Member Rating: 3.9


(1)
Message 230 of 292 (684583)
12-18-2012 12:21 AM
Reply to: Message 229 by JonF
12-17-2012 6:21 PM


Re: U-Pb, Pb-Pb, And Fission Track Dating
OK, I've edited the article, is that better or do you have to slap me around some more?

Thanks again.


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JonF
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Message 231 of 292 (684675)
12-18-2012 12:07 PM
Reply to: Message 230 by Dr Adequate
12-18-2012 12:21 AM


Re: U-Pb, Pb-Pb, And Fission Track Dating
Looks good. I still think some mention of discordia, perhaps in another installment, would be worthwhile.
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Dr Adequate
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Posts: 15485
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Message 232 of 292 (684867)
12-19-2012 3:05 AM


Radiocarbon Dating
Radiocarbon dating

Introduction

In this article we shall discuss how radiocarbon dating works, the conditions under which it can be applied, and the limitations of the method.

The isotopes

There are three important isotopes underlying the process of radiocarbon dating.

14N (nitrogen-14) is converted to 14C (carbon-14) in the upper atmosphere as a result of bombardment by neutrons in so-called cosmic rays: high-energy particles bombarding the Earth's atmosphere from outer space. Such an isotope is said to be cosmogenic. On formation, the newly-born carbon atom quickly oxidizes to form a molecule of carbon dioxide (CO2).

14C is an unstable isotope of carbon, and so decays back to 14N via beta decay with a half-life of about 5730 years. Because the quantity of 14C being produced annually is more or less constant, whereas the quantity being destroyed is proportional to the quantity that exists, it can be shown that the quantity in the atmosphere at any given time will be more or less constant: the processes of production and decay of 14C produces an equilibrium.

Also of importance is the stable carbon isotope 12C; this makes up 98.89% of atmospheric carbon, as opposed to only 0.0000000001% 14C. The balance is made up by the stable isotope 13C, which need not concern us in this article.

The terrestrial carbon cycle

The terrestrial carbon cycle is fairly simple: plants get their carbon from the atmosphere via the process of photosynthesis; herbivores get their carbon from plants, and carnivores from the herbivores. After the death of the organism, processes of decay will return its carbon to the atmosphere, unless it is sequestered --- for example in the form of coal.

This means that when an organism is alive, its ratio of 14C/12C will be the same as the ratio in the atmosphere. But of course when the organism dies it is cut off from the source of atmospheric carbon, the 14C will start to decay to 14N, and the ratio will begin to change.

The method

This immeditately suggests a method of dating organic remains. If we measure the amount of 12C and the amount of 14C in an organic sample, then since we know the atmospheric ratio and the amount of 12C present, we can deduce how much 14C was present originally. And then since we know how much was present originally, since we can measure how much is present now, and since we know the decay rate of 14C, it is trivial to compute the age of the sample.

This method is variously known as radiocarbon dating, carbon dating, 14C dating, or C-C dating.

One of the nice things about this method is that we don't have to worry about carbon being lost from the sample. Because we are measuring the abundance of two isotopes of carbon, and because isotopes of the same element will be chemically identical, no ordinary process can preferentially remove 12C or 14C, and so any process of carbon removal will leave the 12C/14C ratio the same, and the method will still work.

Limitations of the method

The method has various limitations. First of all, the quantity of 14C is going to be small enough to begin with, being only 0.0000000001% of atmospheric carbon, and then as the decay process progresses, it's going to get smaller and smaller. After about 60,000 years, the quantity will be too small for our instruments to measure accurately, and the best we'll be able to say is that the sample is about 60,000 years old or more. For this reason radiocarbon dating is of more interest to archaeologists than to geologists.

Two effects also interfere with the dating of very recent samples. The testing of thermonuclear weapons produced an increase in atmospheric 14C, peaking in the mid-1960s; and the burning of fossil fuels has been causing an increase in atmospheric 12C; this has not been accompanied by a corresponding increase in 14C because as the carbon in coal and oil is old, the amount of 14C they contain is infinitesimal. Fortunately it is rarely necessary to use radiocarbon methods to date very recent samples.

Thirdly, it is in the nature of the method that it can only be applied to organic remains: it makes no sense to apply it to rocks or to mineralized fossils.

Fourthly, the carbon in the organic remains does have to originate with the terrestrial carbon cycle and with plants performing photosynthesis. If this is not the case, it is sometimes possible to correct for the fact; in other cases it makes dating impossible.

For example, marine carbon behaves quite differently from carbon in the terrestrial cycle. The residence time of carbon in the ocean can be measured in hundreds of thousands of years (where the residence time of carbon is defined as the average time an atom of carbon will stay in the ocean). This increases the apparent age of the sample by about 400 years, depending on where in the ocean the organism lived and died. Given a latitude and longitude, an appropriate correction to the date is supplied by the Marine Reservoir Database.

Since humans eat seafood, this can also affect the carbon dating of humans, and what is worse it does so in an inconsistent manner, since human consumption of seafood varies with location and culture. However, the marine component of diet can be estimated by measuring the ratio of the stable isotopes 15N/13C in the sample: this will be higher the more seafood the individual consumed. This allows archaeologists to estimate the magnitude of this effect and correct for it.

Another source of carbon we have to take into account is the weathering of limestone. The result of this is to supply streams, rivers, and lakes with a source of dissolved calcium carbonate; if freshwater shellfish (for example) use this to construct their shells, then they are using a source of carbon which is millions of years old. Clearly applying radiometric dating in such a case is pointless. Another source of old carbon is the outgassing from volcanoes: in locations where this is a significant source of CO2, plants growing in the area will appear older than they actually are.

Even participation in the terrestrial carbon cycle does not quite guarantee the date: we could, for example, imagine termites eating their way through the wood of a 200 year old house; these termites would date to 200 years old or more (depending on the age of the tree). By and large, however, organisms tend to consume fresh vegetation or fresh meat, so this problem is unlikely to arise in practice.

Comparison with known dates

One way we can check the efficacy of radiocarbon dating is to compare the dates it produces with dates known on historical grounds, to ensure that it does indeed give us the right answer. The graph below shows the results obtained by the pioneer of the method, W.F. Libby, showing the measurements of 14C made on artifacts of known date compared with what would be expected on the basis of their dates as known on historical and archaeological grounds.

The fit is quite good, as you can see, even though the measurements were made in the infancy of the science when measuring techniques were inferior to those in use today and the half-life of 14C was not known so accurately as is now the case.

We can also compare radiocarbon dates with dates known on other grounds. For example, we have discussed the use of varves for dating; now since varves incorporate organic material as they are formed, we can check that when we radiocarbon date a varve, we get the same date for it as we obtain by counting the varves.

Again, it is obviously possible to carbon-date one of the rings of a tree, and to compare the date produced by radiocarbon dating with the date produced by dendrochronology. Such dates typically agree to within 1 or 2 per cent.

Calibrated dating

Although the radiocarbon dates agree closely with dendrochronology, they do not agree exactly. It is generally agreed that the dendrochronological dates should be considered the more accurate. The proportion of 14C in the atmosphere is not absolutely constant; for example, it can be reduced by volcanic activity, since the carbon dioxide emitted by volcanoes is richer in 12C than atmospheric carbon dioxide. By comparison the behavior of the genera of trees used in dendrochronology is more reliable and consistent.

It is therefore standard procedure to tweak the raw radiocarbon dates to bring them in line with dendrochronology, producing what are known as calibrated radiocarbon dates. This allows us to combine the greater accuracy of dendrochronology with the wider applicability of radiocarbon dating.

Edited by Dr Adequate, : No reason given.

Edited by Dr Adequate, : No reason given.


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Coyote
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Message 233 of 292 (684900)
12-19-2012 9:37 AM
Reply to: Message 232 by Dr Adequate
12-19-2012 3:05 AM


Re: Radiocarbon Dating
This means that there's no sense in trying to carbon date a salt-water fish, a whale, a sea-otter, and so forth.

Actually we date marine organisms all the time. But we do have to include a marine correction factor, which varies from area to area. This is called Delta-R.

For the area I work in that figure is 22535 years. This is in addition to a worldwide marine correction factor that I think is something like 400 years.

But it is always good to test these various corrections against one another.

We encountered a feature in an archaeological site a few years ago consisting of three nestled abalone shells (face up), and in the upper shell we found both halves of a large mussel shell and charcoal. Capping this we found two more abalone shells, face down.

We dated one abalone shell, one mussel shell, and the carbon. When all corrections and calibrations were applied the three dates spanned 14 years.


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RAZD
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Message 234 of 292 (684912)
12-19-2012 10:36 AM
Reply to: Message 232 by Dr Adequate
12-19-2012 3:05 AM


Re: Radiocarbon Dating - reservoir effect
Hi Dr Adequate,

To add to what Coyote said:

Marine carbon behaves quite differently from carbon in the terrestrial cycle. The residence time of carbon in the ocean can be measured in hundreds of thousands of years (where the residence time of carbon is defined as the average time an atom of carbon will stay in the ocean). ...

This is called the "reservoir effect" and it can be calibrated to obtain corrected results as well:

http://www.c14dating.com/corr.html

quote:
Reservoir effects

Radiocarbon samples which obtain their carbon from a different source (or reservoir) than atmospheric carbon may yield what is termed apparent ages. A shellfish alive today in a lake within a limestone catchment, for instance, will yield a radiocarbon date which is excessively old. The reason for this anomaly is that the limestone, which is weathered and dissolved into bicarbonate, has no radioactive carbon. Thus, it dilutes the activity of the lake meaning that the radioactivity is depleted in comparison to 14C activity elsewhere. The lake, in this case, has a different radiocarbon reservoir than that of the majority of the radiocarbon in the biosphere and therefore an accurate radiocarbon age requires that a correction be made to account for it.

One of the most commonly referenced reservoir effects concerns the ocean. The average difference between a radiocarbon date of a terrestrial sample such as a tree, and a shell from the marine environment is about 400 radiocarbon years (see Stuiver and Braziunas, 1993). This apparent age of oceanic water is caused both by the delay in exchange rates between atmospheric CO2 and ocean bicarbonate, and the dilution effect caused by the mixing of surface waters with upwelled deep waters which are very old (Mangerud 1972). A reservoir correction must therefore be made to any conventional shell dates to account for this difference. Reservoir corrections for the world oceans can be found at the Marine Reservoir Correction Database, a searchable database online at Queen's University, Belfast and the University of Washington. Human bone may be a problematic medium for dating in some instances due to human consumption of fish, whose C14 label will reflect the ocean reservoir. In such a case, it is very difficult to ascertain the precise reservoir difference and hence apply a correction to the measured radiocarbon age.


I have referred to this site before in answer to a creationist claim(1) about dating a modern seal at McMurdo Sound (Antarctica) with an apparent age in thousands of years. Looking up the area in question gave me a reservoir effect that brought the seal age back into modern times with proper calibration.

Although the radiocarbon dates agree closely with dendrochronology, they do not agree exactly.

The corrected dates are generally older than the uncorrected dates. A calibration curve from dendrochronology is (2):

14C is an unstable isotope of carbon, and so decays back to 14N via beta decay with a half-life of about 5730 years. Because the quantity of 14C being produced annually is more or less constant, whereas the quantity being destroyed is proportional to the quantity that exists, it can be shown that the quantity in the atmosphere at any given time will be more or less constant: the processes of production and decay of 14C produces an equilibrium.

I would say that it tends towards an equilibrium, but oscillates around a stable value due to the variation in production. These variations appear in the calibration curve as the jagged bumps in the dendro data.

Enjoy

(1) - see claim at http://www.talkorigins.org/indexcc/CD/CD011_4.html

(2) - see 14C Calibration and Correlations for more


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This message is a reply to:
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Coyote
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Message 235 of 292 (684915)
12-19-2012 10:45 AM
Reply to: Message 234 by RAZD
12-19-2012 10:36 AM


Re: Radiocarbon Dating - reservoir effect
In the quotation RAZD included above was the statement:

Human bone may be a problematic medium for dating in some instances due to human consumption of fish, whose C14 label will reflect the ocean reservoir. In such a case, it is very difficult to ascertain the precise reservoir difference and hence apply a correction to the measured radiocarbon age.

By using the ratios between C13 and N15 you can estimate the amount of marine carbon in a bone sample, and can then apply the appropriate correction.

As an example, we analyzed one skeleton with an estimated 92% marine carbon in the diet, so we obviously had to include that factor into the calibration. That correction changed the age by several hundred years.


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JonF
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Message 236 of 292 (684930)
12-19-2012 11:38 AM
Reply to: Message 232 by Dr Adequate
12-19-2012 3:05 AM


Re: Radiocarbon Dating
It might be nice to include U-Th disequilibrium dating of coral in the calibration section. Tree rings only get you to about 12,400 years BP. I happen to think that U-Th disequilibrium dating is a very clever method. It's been used to date corals, bones (exposed to groundwater containing U), a plaster stalactite in the Siloam tunnel in Jerusalem, and more. But you may not want to go into detail of how it works. Wikipedia has reasonably good and short article.

FWIW. the Marine Reservoir Correction Database covers the whole world.


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Dr Adequate
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Posts: 15485
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Message 237 of 292 (685022)
12-20-2012 2:18 AM


Radiocarbon Etc
Lot of interesting suggestions here. Thanks. I shall expand the article on radiocarbon.

I shall be mentioning U-Th in a later article --- I felt it belonged with Th-Pa and Ra-Pb rather than with U-Pb and Pb-Pb.


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JonF
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Message 238 of 292 (685109)
12-20-2012 3:04 PM
Reply to: Message 237 by Dr Adequate
12-20-2012 2:18 AM


Re: Radiocarbon Etc
OK, I just suggest that when you do get to U-Th you refer back the the 14C calibration.
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Dr Adequate
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Posts: 15485
Joined: 07-20-2006
Member Rating: 3.9


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Message 239 of 292 (685161)
12-20-2012 5:34 PM


Cosmogenic Surface Dating
Cosmogenic surface dating

Introduction

In the article we shall discuss the techniques and applications of cosmogenic surface dating.

Applications

Unlike other dating methods, which tell us how long it is since a rock was formed, cosmogenic surface dating tells us how long a rock has been exposed on the surface.

In some cases, as when the rock is a lava flow, this amounts to the same thing. But there are other ways in which a rock can become exposed, as for example when a glacier erodes the topsoil covering bedrock: when the glacier melts, the bedrock will be exposed.

Cosmogenic isotopes

In the article on radiocarbon dating we have already introduced one cosmogenic isotope, 14C, which is produced by cosmic rays from 14N.

For cosmogenic surface dating, the two most commonly used isotopes are the cosmogenic isotopes 10Be, which is produced from 16O and which has a half-life of 1.39 million years; and 26Al, which is produced from 26Si and which has a half-life of 717,000 years.

The method

Because the isotopes we're using have a short half-life, it follows that if a rock has been buried for a few million years the quantities of these isotopes will be negligible. But when the rock becomes exposed on the surface, and so exposed to cosmic rays, these cosmogenic isotopes will begin to accumulate in the rock.

The rate at which they do so will depend on a number of factors, including:

* The exposure of the rock. A nearby obstacle such as a mountain will shield the rock from cosmic rays coming from that direction, reducing the creation of cosmogenic isotopes.

* The elevation of the rock. If the rock is on top of a mountain, then the cosmic rays have less atmosphere to travel through to get to the rock, and so more of them will make the journey all the way to the rock without being absorbed in the atmosphere on the way.

* The depth from which we take the sample. Cosmic rays can penetrate a few meters through rock or soil, but the further they travel the more likely they are to be absorbed, so a rock sample will get more exposure to cosmic rays if it is taken from the surface than if it is taken from a meter down.

If we take all the relevant factors into account, and calculate, estimate, or simply measure the amount of cosmic rays a given rock is exposed to per year, and if we measure the quantities of the cosmogenic isotopes in a sample of the rock, then we can figure out how long the rock has been exposed.

Limitations of the method

The quantity of the relevant isotopes in the rock will not simply grow without limit with longer and longer exposure to cosmic rays; rather they will tend towards a maximum. In practice, we are not going to be able to tell the difference between a rock which has reached 99.9% of this maximum and one which has reached 99.99%. Consequently, the practical limit for the use of cosmogenic surface dating seems to be about 10 million years; after that, one old rock looks much like another. The lower limit for application of the method seems to be about ten years, because of practical limits on the accuracy with which we can measure the quantities of the relevant isotopes.

Edited by Dr Adequate, : No reason given.

Edited by Dr Adequate, : No reason given.


  
Dr Adequate
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Message 240 of 292 (687597)
01-14-2013 6:49 AM


U-Th, U-Pa, And Ra-Pb
U-Th, U-Pa, and Ra-Pb

Introduction

In this article we shall discuss three similar methods that can be used to date marine and lacustrine sediments: the U-Th, U-Pa, and Ra-Pb methods.

The isotopes

The methods discussed in this article each require two isotopes: a parent isotope which is soluble (or the commonly occurring compounds of which are soluble) and a radioactive daughter isotope which is not soluble.

The table below shows three such systems together with the half-life of the daughter isotope.

MethodParentDaughterHalf-life
U-Th234U230Th75,000 yrs
U-Pa235U231Pa32800 yrs
Ra-Pb226Ra210Pb22 yrs

The method

The parent isotope will be present dissolved in the ocean or in lakes, but when decay takes place the insoluble daughter isotope will precipitate out as sediment and will form part of the upper layer of marine or lacustrine sediment. It will subsequently be buried in its turn by further sediment, and being radioactive will undergo decay.

Now, if there was absolutely none of the parent isotope present in the sediment, then the calculation would be very simple: when we have dug down through the sediment up to the point where the daughter isotope is only half as abundant as it is on the surface, then we would have dug back through one half-life's worth of time; and in general we could write:

t = h log2(N/Ns)

where

* t is the age of the sediment;
* h is the half-life of the daughter isotope;
* Ns is the quantity of the daughter isotope on the surface layer of sediment;
* N is the quantity of the daughter isotope at the depth we're trying to date.

That would be the simple case: however it will not necessarily be true that there will be none of the parent isotope in the sediment. There may well be some, but this is not a problem, since we can measure the quantity of the parent isotope present in the upper layers of sediment and take this into account in our calculations. The crucial point is that there will be more of the daughter isotope than could be accounted for by the decay of the parent within the sediment.

Note on the use of Ra-Pb

All the methods described here are somewhat limited in their usefulness by the short half-lives of the daughter isotopes. This is particularly true of 210Pb; since it has a half-life of only 22 years, this makes it useless for most geological purposes. However, it can be used to gauge the rates of deposition of marine sediment as an alternative to the use of sediment traps.

This method has a couple of advantages over sediment traps. First, it is quicker: it doesn't take long to obtain a sediment core sample, whereas a sediment trap has to be left in place for at least a year to produce useful results.

Second, use of Ra-Pb allows us to measure the sedimentation that has taken place over the course of a century or so and average it, reducing the effect of annual fluctuations on the figures we obtain.

Alternate use of U-Th

We can make an alternative use of the fact that 234U is soluble and 230Th is not.

First of all, this means that 234U will be incorporated into the structure of marine organisms such as corals. Secondly, it means that 234U will be incorporated into speleothems and 230Th will not, just as with the U-Pb method discussed in the article on U-Pb and related methods.

There is, however, a difference between U-Pb and U-Th: 230Th is radioactive. Whereas this was essential to its use in dating marine sediments, it is actually an inconvenience when dating organic remains or speleothems, since it means that the 230Th will not only be produced by decay, but also destroyed by it.

As a consequence, what happens is that the quantity of 230Th in the sample will tend towards secular equilibrium: the point at which the thorium is being produced at the same rate as it is being destroyed. This fact, combined with the practical difficulty of measuring whether the level of 230Th has reached 99.9%, 99.99%, or 99.999% of secular equilibrium, limits the useful range of the method to about 500,000 years.

Because this method can be applied to organic materials, it can be correlated with the radiocarbon method, and the dates produced by both methods can be shown to be concordant.

Edited by Dr Adequate, : No reason given.

Edited by Dr Adequate, : No reason given.

Edited by Dr Adequate, : No reason given.


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