How do we determine numerical age of Earth?

Numerical age determination

Geologists since the days of Hutton could determine the relative ages of geologic events, but they had no way to specify numerical ages (called “absolute ages” in older literature). Thus, they could not define a timeline for Earth history or determine the duration of events. This situation changed with the discovery of radioactivity. Simply put, radioactive elements decay at a constant rate that can be measured in the lab and can be specified in years. In the 1950s, geologists developed techniques for using measurements of radioactive elements to calculate the numerical ages of rocks. Geologists originally referred to these techniques as radiometric dating; more recently, this has come to be known as isotopic dating. The overall study of numerical ages is geochronology. Since the 1950s, isotopic dating techniques have steadily improved, and geologists have learned how to make very accurate measurements from very small samples. But the basis of the techniques remains the same, and to explain them, we must first review radioactive decay. 

Radioactive Decay 

All atoms of a given element have the same number of protons in their nucleus we call this number the atomic number. However, not all atoms have the same number of neutrons in their nucleus. Therefore, not all atoms of a given element have the same atomic weight (roughly, the number of protons plus neutrons). Different versions of an element, called isotopes of the element, have the same atomic number but a different atomic weight. For example, all uranium atoms have 92 protons, but the uranium-238 isotope (abbreviated 238U) has an atomic weight of 238 and thus has 146 neutrons, whereas the 235U isotope has an atomic weight of 235 and thus has 143 neutrons. Some isotopes of some elements are stable, meaning that they last essentially forever. Radioactive isotopes are unstable in that eventually, they undergo a change called radioactive decay, which converts them to a different element. Radioactive decay can take place by a variety of reactions that change the atomic number of the nucleus and thus form a different element. In these reactions, the isotope that undergoes decay is the parent isotope, while the decay product is the daughter isotope. For example, rubidium-87 (87Rb) decays to strontium-87 (87Sr), potassium-40 (40K) decays to argon-40 (40Ar), and uranium-238 (238U) decays to lead-206 (206Pb). In some cases, decay takes many steps before yielding a stable daughter. Physicists cannot specify how long an individual radioactive isotope will survive before it decays, but they can measure how long it takes for half of a group of parent isotopes to decay. This time is called the half-life of the isotope. 

Figure above (a-c) can help you visualize the concept of a half-life. Imagine a crystal containing 16 radioactive parent isotopes. (In real crystals, the number of atoms would be much larger.) After one half-life, 8 isotopes have decayed, so the crystal now contains 8 parent and 8 daughter isotopes. After a second half-life, 4 of the remaining parent isotopes have decayed, so the crystal contains 4 parent and 12 daughter isotopes. And after a third half-life, 2 more parent isotopes have  decayed, so the crystal contains 2 parent and 14 daughter isotopes. For a given decay reaction, the half-life is a constant.

Isotopic Dating 

Techniques Since radioactive decay proceeds at a known rate, like the tick-tock of a clock, it provides a basis for telling time. In other words, because an element’s half-life is a constant, we can calculate the age of a mineral by measuring the ratio of parent to daughter isotopes in the mineral. In practice, how can we obtain an isotopic date? First, we must find the right kind of elements to work with. Although there are many different pairs of parent and daughter isotopes among the known radioactive elements, only a few have long enough half-lives, and occur in sufficient abundance in minerals, to be useful for isotopic dating. 

Table above lists particularly useful elements. Each radioactive element has its own half-life. (Note that carbon dating is not used for dating rocks because appropriate carbon isotopes occur only in organisms and radioactive carbon has a very short half-life). Second, we must identify the right kind of minerals to work with. Not all minerals contain radioactive elements, but fortunately some fairly common minerals do. Once we have found the right kind of minerals, we can set to work using the following steps. 

• Collecting the rocks: We need to find un-weathered rocks for dating, for the chemical reactions that happen during weathering may lead to the loss of some isotopes. 
• Separating the minerals: The rocks are crushed, and the appropriate minerals are separated from the debris. 
• Extracting parent and daughter isotopes: To separate out the parent and daughter isotopes from minerals, we can use several techniques, including dissolving the minerals in acid or evaporating portions of them with a laser. 
• Analyzing the parent-daughter ratio: Once we have a sample of appropriate atoms, we pass them through a mass spectrometer, an instrument that uses a strong magnet to separate isotopes from one another according to their respective weights (figure below). The instrument can count the number of atoms of specific isotopes separately. 

At the end of the laboratory process, we can define the ratio of parent to daughter isotopes in a mineral, and from this ratio calculate the age of the mineral. Needless to say, the description of the procedure here has been simplified in reality, obtaining an isotopic date is time-consuming and expensive and requires complex calculations.

What Does an Isotopic Date Mean? 

At high temperatures, atoms in a crystal lattice vibrate so rapidly that chemical bonds can break and reattach relatively easily. As a consequence, isotopes can escape from or move into crystals, so parent-daughter ratios are meaningless. Because isotopic dating is based on the parent-daughter ratio, the “isotopic clock” starts only when crystals become cool enough for isotopes to be locked into the lattice. The temperature below which isotopes are no longer free to move is called the closure temperature of a mineral. When we specify an isotopic date for a mineral, we are defining the time at which the mineral cooled below its closure temperature. With the concept of closure temperature in mind, we can interpret the meaning of isotopic dates. In the case of igneous rocks, isotopic dating tells you when a magma or lava cooled to form a solid, cool igneous rock. In the case of metamorphic rocks, an isotopic date tells you when a rock cooled from a metamorphic temperature above the closure temperature to a temperature below. Not all minerals have the same closure temperature, so different minerals in a rock that cools very slowly will yield different dates. Can we isotopically date a clastic sedimentary rock directly? No. If we date minerals in a sedimentary rock, we determine only when these minerals first crystallized as part of an igneous or metamorphic rock, not the time when the minerals were deposited as sediment nor the time when the sediment lithified to form a sedimentary rock. For example, if we date the feldspar grains contained within a granite pebble in a conglomerate, we’re dating the time the granite cooled below feldspar’s closure temperature, not the time the pebble was deposited by a stream.

Other Methods of Determining Numerical Age

The rate of tree growth depends on the season. During the spring, trees grow rapidly and produce lighter, less-dense wood, but during the winter trees grow slowly or not at all, and produce darker, denser wood. Thus, wood contains recognizable annual growth rings. Such tree rings provide a basis for determining age. If you've ever wondered how old a tree that’s just been cut down might be, just look at the stump and count the rings. Notably, by correlating clusters of distinctive rings in the older parts of living trees with comparable clusters of rings in dead logs, scientists can extend the tree-ring record back for many thousands of years, allowing geologists to track climate changes back into prehistory. Seasonal changes also affect rates of such phenomena as shell growth, snow accumulation, clastic sediment deposition, chemical sediment precipitation, and production of organic material. Geologists have learned to use growth rings in shells, as well as rhythmic layering in sediments and in glacial ice (figure above a–c), to date events numerically back through recent Earth history.

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