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Permalink Reply by Nelson on July 17, 2012 at 12:02pm

*3 isotopes of Carbon: C12, C13, and C14

*C12 and C13 are stable and common. C14 is unstable. It is created in the upper atmosphere as a consequence of interaction with cosmic rays from the Sun. It undergoes radioactive decay.

*Isotopes undergoing radioactive decay have what's called a "half life". This is the time it takes for half of a given sample of the isotope to decay. In the case of C14 it's 5,730 years. (Other radioisotopes take far longer. U238's half life is 4.5 billion years)

*Plants, in the course of photosynthesis, take up carbon dioxide and release oxygen. Some of this CO2 is made up of C14. Once plants die they cease taking up C14. So the level of C14 is locked in the sample at its death.

*The level of C14 in the atmosphere available for uptake varies over time and at a given locality but is known and adjusted for ("calibrated").

*Hence, the measure of the remaining C14 in a sample is directly related to the time since the plant died.

Limitations are of course:

1. With a comparatively short half-life, C14 dating can only be used to date things up to a maximum of about 60,000 years. Anything older than that requires radiometric dating using a different radioisotope. Options are U234 with a half-life of 80,000 years and protactinium231 with a half-life of 34,300 years.

2. It can only be used to date samples that either consist of plant matter or that are associated with plant matter. For instance, certainly you can date plant matter itself. But you can also date a human cave settlement by dating the trash heap located in the cave consisting of plant matter, though obviously with wider error bars.

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Permalink Reply by Nelson on July 17, 2012 at 12:46pm

How do they determine this rock or bone is over 5,000 years old vs a rock or bone that is 5,000,000 years old?

As above, anything that is plant matter or that is associated with plant matter can be dated using C14 dating up to about 60,000 years. Samples believed to be older are dated using other methods. In the case of a rock, the rock's age will be determined depending on what type of rock it is. In the case of igneous rocks (rocks formed from cooling magma), dating is often determined using the Potassium-Argon method. When the rock cooled from its liquid state crystals formed. Measurements of the ratio of Potassium and Argon present tell us how long it's been since the crystals formed (that is, since the magma cooled and the rock formed). Dating samples of 5 million year old bone presents a different challenge. Fossilized bone forms in sedimentary rock. First, we don't have the kind of crystals forming in sedimentary rock that we do in igneous. And even the crystals of rock that make up the grains that sedimentary rock consists of would have formed at varying times owing to the nature of sediment in the first place. So that's out. In this case scientists simply look to the brackets of igneous rock that occur below and above the sample of sedimentary rock. Dating these layers gives us a high and low bracket. The bone, then, must date to somewhere in the middle. Through experience and real indicators (like how close the bone actually appears to either one or the other bracket), scientists can get pretty fine estimates of the age of bone using this method.

How precise is this science?

Utterly precise. C14 dating, for instance, can produce dates with an uncertainty as small as 30 years. But I think what you probably mean is how confident are we in the underlying science, not how precise are the measurements themselves. The answer to that question is that if radiometric dating is wrong, then everything we know about physics, plant biology, and geology is wrong. And since our understanding of these things exist in a web of interconnected ideas, each one producing a check against the other, at this point it would be utterly unthinkable that radiometric dating would be overturned. There's just too much confirmation. To say nothing of things like ice cores and tree ring dating providing checks against C14 dates providing confirmation of the accuracy of C14 dating.

Can there be false positives?

Once you understand how the methods work, it's hard to see how there could be. Certainly it is the case that there are uncertainties when it comes to the dating of any given sample. Small fluctuations in the amount of C14 present, locally higher concentrations of a radioisotope at the time of the formation of igneous rock, etc. But these things are accounted for with calibrations and checks (like ice cores and tree rings I mentioned). Plus, samples in the same rock layers from around the world date to the same period. If by false positive you mean "Do we sometimes date a layer of rock (or a bone appearing in a layer of sedimentary rock bracketed by igneous layers) and find that the age of the sample is wildly older or younger than we assumed would be the case given the age of rocks in that area and the ages of previously dated samples..." And the answer is, barring some sort of contamination in the sample of course, No. Furthermore, often, if it's possible, dating may be determined from multiple methods at the same time, or the same sample dated by 2 or more labs. When the numbers come back, the methods agree with each other (with known uncertainties of course) and the labs agree as well.

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Permalink Reply by Doug Reardon on July 17, 2012 at 8:07pm

Great job Nelson!

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Permalink Reply by Dustin on July 18, 2012 at 11:45am

Nelson has to be a bot.  :)

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Permalink Reply by Eric Turnbull on July 18, 2012 at 4:10pm

Great answer!  One criticism: Include a simple 'in a nutshell' explaination for those of us who aren't on that level of intelligence (I understand most of it, but still a little fuzzy).

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Permalink Reply by Nelson on July 18, 2012 at 4:36pm

No problem Eric! Let me know which areas are a little fuzzy and I'll see if we can go right at them and clear them up. :)

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Permalink Reply by Eric Turnbull on July 18, 2012 at 5:02pm

Well, I'm trying to wrap my head around the half-life of C-14 being 5730 years and that allowing carbon dating to date things back 60,000 years and I'm not much of a math wiz.  I guess another question that goes back to the original post about the accuracy of carbon dating would be more specific.  I've heard that the supposed Shroud of Turin (sp?) was misdated due to a fire in the building where it was being kept.  How would that effect carbon dating if it effects it at all?

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Permalink Reply by Nelson on July 18, 2012 at 5:45pm

Great questions.

So let's throw out the carbon dating figures and make up our own for the sake of simplicity. Then we'll get back to C14 at the end.

Imagine a 1lb block of material and, again, for the sake of simplicity, it's made up completely of an isotope of an element that experiences radioactive decay. Then let's say that this isotope's half-life is 1 year. That means that half the sample will have decayed into daughter elements after 1 year.

So let's test a sample. If we test our sample and find that 50% of the sample is our radioactive isotope and 50% is daughter elements then, given the constraints we put on our hypothetical isotope in my paragraph just above, we can safely say that our sample is a year old. And if we were to test a sample and find instead that 25% of the sample was our isotope and 75% were daughter elements, then we could be confident, again, given our constraints on the hypothetical isotope, that the sample was 2 years old.

We'd know this because, in the first example, half of the material had decayed into daughter elements. And since the "half-life" of an isotope is the time it takes for half the quantity of the isotope originally present to turn into daughter elements, and since our hypothetical isotope's half-life is 1 year...

And in the second example, half of half the sample (50% of 50%) is isotope and the rest is daughter elements. And we know that this is what we would expect after 2 years.

So back to C14 and its half-life of 5,730 years. After 5,730 years a sample with what had a known starting amount of isotope will now have half as much present, with the rest being made up of daughter elements. If we test the sample and find that only 25% remains then we know that the sample is in fact 11,460 years old. And this explains why, by the time a sample is around 60,000 years old, it becomes impractical and unreliable to measure its age using C14 dating: because there's so little C14 left (the decay would have halved the amount present initially more than 10 times by then) that accurately measuring the amount present in the sample adds so much uncertainty to the resulting date that we'd just assume use other methods.

About the Shroud of Turin, the contention of believers in the authenticity of the shroud is that the fire in the Saint-Chapelle Chapel in 1532 in Chambery, France where it was kept at the time contaminated the shroud such that accurate C14 dating is not possible in principle or that the dating performed so far is not accurate. This is false. If the shroud was genuine and actually dated to the 1st century CE, do you know approximately how much 20th century carbon contaminant would need to be present in order to produce a 14th century date (as has been attained) for samples of the shroud?

40 POUNDS!!! That's right. You'd have to dust the (approximately) 20lb shroud with approximately 40 POUNDS of 20th century carbon contaminant in order to get an actual 1st century shroud to date to the 14th century.

**Que laughter** :)

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Permalink Reply by Eric Turnbull on July 19, 2012 at 10:47am

Indeed, I lol'd.  Thanks for the explanation!  I guess I did have a pretty good understanding of isotope decay, but I wasn't entirely sure how far (in amount mearurable) measurements could go. 

I thought the Shroud of Turin scenario was a bit flimsy especially considering the difference in dates and the accuracy of carbon dating.

Again, thanks!

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Permalink Reply by SteveInCO on July 21, 2012 at 5:36am

Let me follow this example further, to illustrate the complications that arise when using this one-year-half-life radioisotope to date something in the real world.  I said that these were complications, and they do make it more complicated.  But they do not invalidate the dating.

First off you are never going to be dating something that used to be a pure block of the isotope in question.   It will be a mixture of chemicals.  Also, it's more than likely that the isotope we are talking about is only one of several isotopes of that element.  Let's say it's potassium; there's a stable isotope and then there's the one that decays with a half-life of a year.  The two isotopes behave identically, when it comes to chemistry; they form the same compounds, the same minerals.  Or it could be carbon.  It will turn out that there are special considerations for each case,

Potassium really does have a stable and an unstable isotope, and it exists in a lot of rocks.  The rocks form as minerals crystallize, usually underground but sometimes in lava flows.  At the time the rock forms, there's no difference between the stable potassium and the unstable potassium.  But the unstable isotope turns into argon.  Now argon and potassium are about as unalike as possible; potassium is a solid metal that is so reactive that even water oxidizes it.  Argon is a gas that doesn't react with anything; in fact it forms 1% of the air that's in your lungs right now, with no ill effect.  So when the unstable potassium in the rock decays, it becomes argon, and you can assume that any argon in the rock today used to be potassium, since surely argon would not have combined with the other elements in the rock to begin with.  (I suppose it's possible some argon could be dissolved in the lava, but I have no doubt they know how to account for this.)  So count the atoms of unstable potassium and argon in the rock, and you have your ratio.  (The example I gave elsewhere (at the end of this thread) of the uranium-lead decay is a bit more straightforward, because you simply won't have original lead dissolved in zircon crystals to potentially mess things up)

Carbon-14 is a lot trickier.  It is in organic tissue and decays into perfectly ordinary nitrogen, which is also in organic tissue.  It's very hard to figure out a ratio when you simply don't know which nitrogen used to be carbon-14 and which did not.  What they do instead, as I understand it, is to calculate the ratio of stable carbon to carbon-14 and then compare that to what we have in the atmosphere today.  For example, if five atoms in every billion carbon atoms in the sample is carbon 14, but ten atoms in one billion carbon in the atmosphere is carbon 14, then since carbon 14 is only half as common in the sample, we figure half of what was originally there when the tree or critter died, has since decayed away, and we date the object as having died 5760 years ago.

But that relies on an assumption that we know isn't quite true; that carbon 14 ratios in the atmosphere are constant.  In fact we know that they tend to vary a tiny bit.  Maybe back when the thing died there were 12 atoms per billion, in which case it took a little longer to decay down to the five we measure today.  Maybe back when it died, there were only nine atoms per billion, in which case it took less time to get down to five.  That's where the calibration comes in.  We can, in some special circumstances, date things by other methods, for example we can often date based on patterns of thick and thin tree rings.  This particularly thick ring may be from 1738 which was really rainy.  Sometimes they can build a tree ring sequence that goes back thousands of years, back before "creation" according to the creationists.

Well, measure the carbon in those tree rings, which are already of known age and you might find that the sample with 5 atoms per billion is from a tree ring 6130 years old, not 5760.  So when you have an unknown sample with the same results, you know that it's 6130 years old, not 5760.

That's what it means to "calibrate" carbon 14 dates.

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Permalink Reply by John Major on July 17, 2012 at 2:46pm

@Sophie. Nelson has given a full explanation there. It's covered quite well in the Richard Dawkin's book, 'The Greatest Show on Earth.'

Incidentally, the book also explains dendrochronology. This is dating using tree rings! That allows dating to within one year and is possible now going back 11,000 years!

http://en.wikipedia.org/wiki/Dendrochronology

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Permalink Reply by Reg The Fronkey Farmer on July 17, 2012 at 3:47pm

We know the number of particles that are present when a radioactive element is complete. It decays at a constant rate – that is, it loses half of it energy (mass) over a fixed period of time. We call this the “half-life” of the element. If it has a half-life of 10,000 years then after 5000 years it has half the number of particles left. Then after 2500 years it would have ¼ of the original left and so on. The environment – temperature, soil erosion or any other factor has no effect on the rate of decay. Some elements have very long half-lives and others very short ones. However they can all be seen as types of “atomic clocks” as their decay (loss of energy or mass) is constant and we can work back to see how old something is. Carbon dating is just one form of radioactive decay and is used to date organic material. Other elements date non organic material. Sometimes called “clocks in the rocks.” As mentioned above the Dawkins books has a very good chapter on it.

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