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## Half Life and Radiometric Dating . Texas Gateway

Perhaps the most widely used evidence for the theory of evolution through natural selection is the fossil record. The fossil record may be incomplete and may never fully completed, but there are still many clues to evolution and how it happens within the fossil record. One way that helps scientists place fossils into the correct era on the geologic time scale is by using radiometric dating. Also called absolute dating, scientists use the decay of radioactive elements within the fossils or the rocks around the fossils to determine the age of the organism that was preserved. This technique relies on the property of half-life.

Since U has a half-life of 4. In a sample of rock that does not contain appreciable amounts of Pb, the most abundant isotope of lead, we can assume that lead was not present when the rock was formed.

Therefore, by measuring and analyzing the ratio of UPb, we can determine the age of the rock. This assumes that all of the lead present came from the decay of uranium If there is additional lead present, which is indicated by the presence of other lead isotopes in the sample, it is necessary to make an adjustment.

Potassium-argon dating uses a similar method. K decays by positron emission and electron capture to form Ar with a half-life of 1.

If a rock sample is crushed and the amount of Ar gas that escapes is measured, determination of the ArK ratio yields the age of the rock. Other methods, such as rubidium-strontium dating Rb decays into Sr with a half-life of As ofthe oldest known rocks on earth are the Jack Hills zircons from Australia, found by uranium-lead dating to be almost 4. An ingenious application of half-life studies established a new science of determining ages of materials by half-life calculations. After one half-life, a 1.

Present day estimates for the age of the Earth's crust from this method is at 4 billion years. This radioactivity approach can be used to detecting fake wine vintages too. Isotopes with shorter half-lives are used to date more recent samples. Chemists and geologists use tritium dating to determine the age of water ocean and fresh. In addition, tritium dating can be useful in determining the age of wines and brandies.

The half-life of an isotope is used to describe the rate at which the isotope will decay and give off radiation. Using the half-life, it is possible to predict the amount of radioactive material that will remain after a given amount of time. Its half-life is approximately years. Learning Objectives Describe what is meant by the term half-life and what factors affect half-life.

Calculate the amount of radioactive material that will remain after an integral number of half-lives.

The technique of comparing the abundance ratio of a radioactive isotope to a The isotope 14C is radioactive, and beta-decays with a half-life of 5, years. For example, carbon has a half-life of 5, years and is used to measure the age of organic material. The ratio of. Theoretically, if one could detect the amount of carbon in an object, one could establish that object's age using the half-life, or rate of decay, of the isotope.

Calculate the age of a material based upon its half-life. Describe how carbon is used to determine the age of carbon containing objects. Give examples of other isotopes used in radioactive dating.

## Half-life and carbon dating

Appreciate the half-life of isotopes involved in nuclear weapons and reactors. Rate of Radioactive Decay During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element.

Image used with permission CC-BY 4. Interactive Simulation: Visualizing Half-Life Click on this interactive simulation to visualize what happens to a radioisotope when it decays.

Solution To determine the number of half-lives nboth time units must be the same. Radioactive Dating Radioactive dating is a process by which the approximate age of an object is determined through the use of certain radioactive nuclides.

After death, the C decays and the CC ratio in the remains decreases. Comparing this ratio to the CC ratio in living organisms allows us to determine how long ago the organism lived and died. Solution Radioactive Dating Using Nuclides Other than Carbon Radioactive dating can also use other radioactive nuclides with longer half-lives to date older events.

Summary and Vocabulary The half-life of an isotope is used to describe the rate at which the isotope will decay and give off radiation. Background radiation : Radiation that comes from environment sources including the earth's crust, the atmosphere, cosmic rays, and radioisotopes.

These natural sources of radiation account for the largest amount of radiation received by most people. Half-life : The half-life of a radioactive substance is the time interval required for a quantity of material to decay to half its original value.

And what is one mole of carbon? That's 6. This is a ginormous number. This is more than we can, than my head can really grasp around how large of a number this is.

And this is only when we have 12 grams. For example, one kilogram is about two pounds.

## Nuclear Chemistry: Half-Lives and Radioactive Dating

So this is about, what? 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. 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.

And it does that by releasing an electron, which is also call a beta particle. We could have written this as minus 1 charge.

Relatively zero mass. 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.

Scientists look at half-life decay rates of radioactive isotopes to estimate when a particular atom might decay. A useful application of half-lives is radioactive. Archaeologists use the exponential, radioactive decay of carbon 14 to This half life is a relatively small number, which means that carbon 14 dating is not. Explain radioactive half-life and its role in radiometric dating; Calculate radioactive half-life and solve problems associated with radiometric dating.

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. And it really shouldn't be drawn this way.

How Does Radiocarbon Dating Work? - Instant Egghead #28So let me redraw it. So this is our original block of our carbon What happens over that 5, years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if you go back after a half-life, half of the atoms will now be nitrogen. So now you have, after one half-life-- So let's ignore this. So we started with this.

All 10 grams were carbon. This is after one half-life.

Radiocarbon dating is a method for determining the age of an object containing organic .. Calculating radiocarbon ages also requires the value of the half-life for C. In Libby's paper he used a value of ± 47 years, based on. There are several reasons why, but the main reasons is that Carbon is a naturally occurring isotope in all forms of life and its half-life is.

And now we have five grams of c And we have five grams of nitrogen Fair enough. Let's think about what happens after another half-life. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon So let me actually copy and paste this one.

# Carbon dating and half life

This is what I started with. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here. Let me clean it up a little bit. After one one half-life, what happens? Well I now am left with five grams of carbon And by the law of large numbers, half of them will have converted into nitrogen So we'll have even more conversion into nitrogen So now half of that five grams.

So now we're only left with 2. And how much nitrogen? Well we have another two and a half went to nitrogen. So now we have seven and a half grams of nitrogen