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Dating the Earth Study Guide (page 2)

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Atomic Clocks

How old is the earth and its various rocks? How can geologists be so sure when they say that a given igneous layer of rock is 200 million years old, or 1.5 billion years old?

One early attempt to date geological time used the ocean's salinity. We know how much salt goes into the ocean by the world's rivers. We also know the total amount of salt in the ocean. Assuming that the flows of rivers have stayed approximately constant over long periods of time, and assuming that the ocean started off as fresh water, one might compute how long the rivers have been carrying salt to the ocean. In 1889, the answer was first calculated as 90 million years. That's a long time but still way too low, compared to our modern values for the scale of geological time. (Some of the assumptions were not good.)

Modern accurate methods use atomic clocks. The key concept to understanding these clocks is the fact that the radioactive breakdown of certain isotopes occurs at a known rate. First, we will review isotopes and radioactive decay. Then we will discuss how these facts are used in geological dating.

Recall that atoms of a particular element all have the same number of protons in their nuclei. Further more, the number of protons determine the charge of each nucleus, thus the number of electrons around each nucleus, and thus the chemistry of the element. But atoms of elements can vary in the number of neutrons in their nuclei. These variants are called isotopes.

Here's an example. The element carbon comes in three isotopes: carbon-12, carbon-13, and carbon-14. Most of the carbon in your body is carbon-12, a stable isotope with six protons and six neutrons in the atomic nucleus. Carbon-13 is also a stable isotope with six protons and seven neutrons in its nucleus. Finally, we come to carbon-14, a radioactive isotope (sometimes called a radioisotope). The atomic nucleus of carbon-14 has six protons and eight neutrons.

A stable isotope is an atom whose nucleus stays the same, basically forever. A radioactive isotope is different in that the energy balance in the nucleus between protons and neutrons is not right and the nucleus will undergo radioactive decay. At some point in time, that is randomly determined. The nucleus spontaneously shifts to a new form during radioactive decay, in the direction of more stability. Five different kinds of radioactive decay exist, but the details of all five do not concern us here. It is enough to know that in the case of carbon-14, one neutron in the nucleus will spontaneously transform into a proton, with the emission of an electron.

Note that in the case of the radioactive decay of carbon-14, when the neutron changes into the proton, the resulting new nucleus, instead of the six protons and eight neutrons of carbon-14, now has seven protons and seven neutrons. The atomic element itself has changed, from carbon with six protons, into nitrogen with seven protons. The electron that is shot out of the decaying atom's nucleus is energy given off by the nuclear transformation, and the electron can be recorded by human instruments.

A remarkable fact has been discovered from measuring the number of decay events from a mass of radioactive isotopes (for example, measuring the rate of electrons given off by a mass of carbon-14). The number of decay events is proportional to the mass. In other words, doubling the mass doubles the number of decay events. Cutting the mass to one-quarter cuts the decay events to one-quarter. This fact seems simple, but as we will see, it has profound implications for measuring the ages of rocks.

Let us consider, then, a particular mass M of some radioisotope, say, of carbon-14. It decays at a rate R (measured as R number of events per second). Because the carbon-14 turns into nitrogen as it decays, the mass of the carbon-14 decreases over time. As some point, it reaches a mass 0.5 M, or half its original mass M. At that time, the decay rate will also be half and equal to 0.5 R. Now more time passes, and as atoms of carbon-14 one by one turn into nitrogen, eventually the mass 0.25 M is reached. At that time, the decay rate is 0.25 R.

Theory shows this fact to be true and measurements have verified it: The time it takes for M to change to 0.5 M is the same time it takes for 0.5 M to change to 0.25 M. In other words, the amount of time it takes for any given amount of mass to decay to half that mass is always the same. This time is called the half-life. The half-life is the amount of time taken for half the atoms in a mass of radioactive atoms to undergo nuclear decay.

The half-life varies for different radioactive elements. Here are some examples for a few of the radioactive elements that have been proven most useful for dating geological times: carbon-14, half-life of 5,730 years; potassium-40, half-life of 1.3 billion years; uranium-238, half-life of 4.5 billion years.

The half-life determines the interval of time over which a certain radioisotope can be useful for dating. For example, carbon-14, with a relatively short half-life, is valuable for dating ruins of the Pueblo Indians of ancient America. They used wood (which contains carbon) to build roofs for their cliff dwellings. In contrast, carbon-14 is not useful for dating rocks a billion years old. First of all, even if such ancient rocks do contain carbon (as the carbonate rocks do), so many half-lives have passed that the amount of carbon-14 left would be not measurable; it would essentially be zero.

To perform the dating of a rock, we would need to know the original mass of a radioisotope that was in the rock at the time of the rock's formation and the current, reduced mass of the radioisotope in the rock. By comparing the masses, we can then compute how many half-lives have passed to lower the original amount of radioisotope to the current amount. For example, if the original amount of carbon-14 in some ancient charcoal is M and the current amount is M, we know that three half-lives have passed (count them: MM/2 → M/4 → M/8). Because we know that the half-life of carbon-14 is 5,730 years, we then know that the sample is 17,190 years old (3 × 5,730 years).

This strategy for calculation works well in the case of carbon-14, because carbon-containing materials (such as wood) started off with about the same ratios of carbon-14 as when they grew during their lives (because the carbon-14 comes from the atmosphere). But in the case of the very important radioisotope potassium-40, which is used for dating rocks, we don't know how much potassium-40 was in the original rock. What can scientists do?

What is done in the case of potassium-40 is to measure not only the current amount of potassium-40 in a rock, but also the amount of argon-40. Why? Argon-40 is a daughter product of potassium-40 radioactive decay. In other words, when potassium-40 undergoes radioactive decay, argon-40 is created. (What is the daughter product of carbon-14? You'll be asked that in one of the practice questions.)

Here's an important fact about igneous rocks. Magma contains no argon-40, because the argon-40 is driven off by heat. Thus, when any ancient rock that contains a mixture of potassium-40 and argon-40 is heated into magma, it loses its argon-40, but it keeps its potassium-40. When the magma solidifies to become a new igneous rock, the atomic clock of potassium-40 is restarted.

Thus, when igneous rock forms, it contains a certain amount of potassium-40 but zero argon-40. Here we must introduce one slight complication to the story of the radioactive decay of potassium-40. Potassium-40 decays into not one but two daughter products. This happens randomly for any given atom, but with perfect regularity for a mass of potassium-40 as a whole. Twelve percent of the decay goes into argon-40 and 88% of the decay goes into calcium-40, but this fact doesn't affect our analysis, because these percentages of daughter products are constant. It doesn't matter what minerals the potassium is in. Neither do the temperatures or pressures.

So let's return to a newly formed igneous rock with an unknown amount of potassium-40 and no (zero) argon-40. Millions or billions of years later, a modern geologist takes a sample of that rock and measures the amounts of both potassium-40 and argon-40. The rock today contains argon-40 because some of the potassium-40 over time has changed into argon-40. So we know that the rock formed with zero argon-40, and we know today's amounts of potassium-40 and argon-40. These numbers are all that are needed to calculate the age of the rock.

We won't do the calculation here, except to layout the logic. Measuring the amount of argon-40 in a piece of igneous rock allows us to calculate how much potassium-40 underwent radioactive decay since the solidification of the rock (using the fact that 12% of the decayed potassium-40 goes to argon). Then, measuring how much potassium-40 is currently in the rock, we can compute how much original potassium-40 was in the rock by adding to the current amount the amount that must have been lost through radioactive decay, computed from the argon-40 measurement.

Then, because we know the original and current amounts of potassium-40, as in our example with carbon-14, we can compute how many half-lives have passed since the igneous rock was formed. Because the half-life of potassium-40 is 1.3 billion years, it is certainly possible that some rocks will have gone through several half-lives of potassium-40 since the time they were born as igneous rocks. But it's even more common, of course, to find igneous rocks not as old as one half-life of potassium-40. That's okay. Scientists can easily measure fractions of a half-life. Indeed, potassium-40 and argon-40 are so useful as a pair of measurements (called potassium-argon dating) for the precise dating of rocks that the measurements can even be used for volcanic rocks as young as 50,000 years old. At the other end of the time scale, potassium-argon dating can measure rocks that go back to the oldest rocks we have on Earth. We can use the various radioisotopes to perform atomic dating to find out when the first rocks on Earth were formed, and it turns out that they are 3.9 billion years old.

When astronauts brought back rocks from the moon, starting in 1969 and for the few years of the Apollo Program, those rocks were dated in laboratories on Earth. The oldest moon rocks (all igneous) are about 4.1 billion years old. Why would the moon rocks be older than rocks on Earth? As we've seen, the moon formed when a rogue body, about the size of Mars, smashed into the earth very early in Earth's history, so you would think their oldest rocks would be about the same age. On Earth, the forces of plate tectonics have continuously reshaped the surface. So we can assume that rocks older than 3.9 billion years did exist at one time on Earth, but none remain on the continents.

The atomic dating can also be used for meteorites that land on Earth from space. Meteorites clock in at about 4.6 billion years old. This well-verified date of the meteorites is taken to be the time when the earth and all the other planets of the solar system condensed out of a huge gas nebula in space, which also formed the sun. So the earth as a planet is 4.6 billion years old or, rounded to the nearest half-billion, about 4.5 billion years old.

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