4. Radioisotope Dating

The world is radioactive, and that has an extremely useful application. In particular, it allows us to determine the age of many different types of materials. When we use an isotope (an element with an unusual number of neutrons in its nucleus) that is radioactive, we say we are obtaining a radioisotope date.

Carbon-14

The first method was invented by Williard Libby in the 1950s. He discovered that radiocarbon, C-14, had a half life of nearly 6000 years. (The actual numbers is closer to 5730 years, but for this course, just remember it is about 6000 years, abbreviated 6 kyr.) [10]

Moreover, although the C-14 on the surface of the Earth is constantly decaying away, it is also being produced. Cosmic rays (high energy protons from space) hit the atmosphere and produce neutrons; these neutrons are absorbed by a nitrogen atom in the atmosphere, which then immediately emits a proton, creating a new C-14. The net effect is that the C-14 is produced at the same rate as it decays, so the level of C-14 stays constant. Its level is one part in a trillion, i.e. 10^-12 of ordinary carbon. [5]

Plants absorb this carbon when they breathe in carbon-dioxide. So the carbon in plants consists of one part in a trillion C-14. We eat plants (and animals that eat plants, and animals that eat other animals) and the result is that the carbon in our bodies is also one part in a trillion C-14. As long as we eat and breathe, our carbon is one trillionth C-14.

When we die, the C-14 decays (with its 6 thousand year half-life) but it is no longer replaced. After you are buried for 6 kyr, the amount of C-14 in your body is reduced by half. In another 6 kyr, it is cut in half again. By measuring the ratio of C-14 to ordinary carbon, we know when you died (or the tree, or the fossil, or whatever).

For example, if we measure that a bone does not have one part in a trillion of carbon, but only 1/8 that much, then we knows it has been buried for 3 half lives. (It is three half lives, because the amount is reduced by 1/2 three time, and 1/2 x 1/2 x 1/2 = 1/8.) Three half lives means it is 18 kyr old. [2]

This method is extremely useful in archeology. Current controversies include the question of when did humans first enter the North American continent. C-14 dates from fossils of humans seem to indicate that they arrived before the last ice age ended. But some groups of Native Americans argue that it is improper to analyze these bones, because they are the bones of their ancestors.

Potassium-40

All potassium contains a 0.01% (i.e. one part in 10,000) of the radioactive isotope K-40. ("K" is the chemical symbol for potassium. K-40 means that the total number of neutrons and protons in the nucleus is 40. Ordinary potassium is K-39.) The half life of K-40 is 1.26 billion years. When it decays (explodes), the K-40 emits an electron, a neutrino, and the remaining nucleus turns into Argon-40, abbreviated Ar-40.

This is particularly useful for geology. Imagine that there was a volcanic eruption in the past, and a molten rock lands in the sea. Because the rock was hot and molten, any gas that was trapped inside it escapes. When the rock solidifies, it initially has no gas trapped inside. But here is potassium inside, and therefore there is also potassium-40 inside. Every year, some of that K-40 decays, turning into argon gas. Because the rock is solid, the gas cannot escape. [11]

This rock might be trapped in sea floor sediment, where it becomes part of newly forming sedimentary rock. A million years later, this sedimentary rock might have been lifted above the sea as mountains formed. We examine the rock, and we see an interesting fossil. Perhaps the fossil of a dinosaur. We wonder how old is the fossil? In the same sedimentary rock, the astute geologist notices a rock that he can tell (he is a geologist!) came from a volcano. He brings the rock to the laboratory, melts it, and measures the amount of argon gas that comes out. From that measurement, the geologist knows how long ago the rock was formed, and so knows when the dinosaur bone was laid down.

It is this method, called Potassium-Argon dating, that has given us the best estimates for the ages of ancient fossils. [2]