# Carbon dating and half lifes

### BioMath: Carbon Dating

Radioactive dating can also use Since U has a half-life of RADIOACTIVE HALF-LIFE (CONTINUED). After this reading this section you will be able to do the following: Describe carbon dating and how half-life. Radiocarbon dating is a method that provides objective age estimates for The CRA conventions include (a) usage of the Libby half-life, (b) usage of Oxalic.

I want to say [? And pounds is obviously force. You get the idea. On Earth, well anywhere, mass is invariant. This is not a tremendous amount. So with that said, let's go back to the question of how do we know if one of these guys are going to decay in some way. And maybe not carbon, maybe we're talking about carbon or something. How do we know that they're going to decay? And the answer is, you don't. They all have some probability of the decaying. At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay.

That, you know, maybe this guy will decay this second. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay. And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic. I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting.

### Carbon - Wikipedia

Now you could say, OK, what's the probability of any given molecule reacting in one second? Or you could define it that way. But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So what we do is we come up with terms that help us get our head around this. And one of those terms is the term half-life. And let me erase this stuff down here. So I have a description, and we're going to hopefully get an intuition of what half-life means.

So I wrote a decay reaction right here, where you have carbon It decays into nitrogen And we could just do a little bit of review.

You go from six protons to seven protons. Your mass changes the same. So one of the neutrons must have turned into a proton and that is what happened.

### Radiocarbon dating - Wikipedia

And it does that by releasing an electron, which is also call a beta particle. We could have written this as minus 1 charge. It does have some mass, but they write zero. This is kind of notation. So this is beta decay. Beta decay, this is just a review. But the way we think about half-life is, people have studied carbon and they said, look, if I start off with 10 grams-- if I have just a block of carbon that's 10 grams.

If I wait carbon's half-life-- this is a specific isotope of carbon. Remember, isotopes, if there's carbon, can come in 12, with an atomic mass number of 12, or with 14, or I mean, there's different isotopes of different elements. And the atomic number defines the carbon, because it has six protons. Carbon has six protons. But they have a different number of neutrons. So when you have the same element with varying number of neutrons, that's an isotope.

So the carbon version, or this isotope of carbon, let's say we start with 10 grams. If they say that it's half-life is 5, years, that means that if on day one we start off with 10 grams of pure carbon, after 5, years, half of this will have turned into nitrogen, by beta decay.

And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? And how does this half know that it must stay as carbon?

And the answer is they don't know.

## Half-life and carbon dating

And it really shouldn't be drawn this way. So let me redraw it. Simplifying this expression by canceling the N0 on both sides of the equation gives. Solving for the unknown, k, we take the natural logarithm of both sides. Thus, our equation for modeling the decay of 14C is given by. Other radioactive isotopes are also used to date fossils.

The half-life for 14C is approximately years, therefore the 14C isotope is only useful for dating fossils up to about 50, years old. Fossils older than 50, years may have an undetectable amount of 14C. For older fossils, an isotope with a longer half-life should be used. For example, the radioactive isotope potassium decays to argon with a half life of 1.

Archaeology and other human sciences use radiocarbon dating to prove or disprove theories. Over the years, carbon 14 dating has also found applications in geology, hydrology, geophysics, atmospheric science, oceanography, paleoclimatology and even biomedicine. Basic Principles of Carbon Dating Radiocarbon, or carbon 14, is an isotope of the element carbon that is unstable and weakly radioactive.

The stable isotopes are carbon 12 and carbon Carbon 14 is continually being formed in the upper atmosphere by the effect of cosmic ray neutrons on nitrogen 14 atoms.

It is rapidly oxidized in air to form carbon dioxide and enters the global carbon cycle. Plants and animals assimilate carbon 14 from carbon dioxide throughout their lifetimes. When they die, they stop exchanging carbon with the biosphere and their carbon 14 content then starts to decrease at a rate determined by the law of radioactive decay. Radiocarbon dating is essentially a method designed to measure residual radioactivity. By knowing how much carbon 14 is left in a sample, the age of the organism when it died can be known.

It must be noted though that radiocarbon dating results indicate when the organism was alive but not when a material from that organism was used. Measuring Radiocarbon — AMS vs Radiometric Dating There are three principal techniques used to measure carbon 14 content of any given sample— gas proportional counting, liquid scintillation counting, and accelerator mass spectrometry. Gas proportional counting is a conventional radiometric dating technique that counts the beta particles emitted by a given sample.

Beta particles are products of radiocarbon decay. In this method, the carbon sample is first converted to carbon dioxide gas before measurement in gas proportional counters takes place.

Liquid scintillation counting is another radiocarbon dating technique that was popular in the s.