In the previous tutorial we learned that prior to the early 1900s, geologists used relative dating to estimate the age of the Earth. These estimates varied dramatically, ranging from millions to billions of years. The main reason for this uncertainty is that there is no accurate way to determine how much missing time unconformities represent, but once radiometric dating was employed, the combination of the two dating methods produced a very detailed and accurate timeline of Earth’s history.
Radiometric dating, or absolute dating, is a method of extracting exact ages from rocks that utilizes the concept of nuclear decay, where radioactive nuclides emit a high energy particle to become a nuclide of some other element. In order for radiometric dating to be applicable, certain prerequisite criteria must be met. Rocks must form and then become closed systems where there is no exchange of atoms between the rock and its environment.
The best rocks with which to use radiometric dating are igneous rocks that cooled quicky and have not been reheated above the blocking temperature, which is the temperature at which parent and daughter isotopes can be lost to the environment. Sedimentary rocks cannot be dated using absolute dating, but their constituent mineral grains can be. For example, in a previous tutorial we mentioned the Jack Hills Conglomerate, which was deposited about 3 billion years ago, but it contains the oldest terrestrial material found on Earth, in the form of 4.
4-billion-year-old zircon crystals. Metamorphic rocks are difficult to date with radiometric dating because the process of metamorphism can involve hot fluids, which can add or remove parent and daughter isotopes that are used to date the rock. But for many rocks it is highly reliable, so let’s learn more about how this works.
Radiometric dating was first documented in 1907 by Dr Bertram Boltwood after he discovered that uranium decays into lead, and that the uranium to lead ratio present in a rock would vary based on the rock’s age. We’ve discussed nuclear decay in some detail over in the general chemistry series, so check out this tutorial if you need a thorough refresher on nuclear stability, nuclear reactions, and applications. Otherwise, let’s reiterate the main concepts and contextualize them.
The utility of radiometric dating is based on the existence of isotopes, or atoms of the same element with differing numbers of neutrons. Carbon, for example, has three naturally-occurring isotopes: carbon-12, carbon-13, and carbon-14. Of these, only carbon-14 is radioactive, due to an unfavorable proton to neutron ratio.
It will therefore break down into nitrogen-14 via beta decay, or the emission of an electron which causes a neutron to become a proton, thereby transmuting the nuclide. All radioactive isotopes decay at a specific rate that is represented by the isotope’s decay constant, or number of disintegrations per year, which can be used to calculate its half-life, or the amount of time it takes for half of the radioactive parent nuclide to decay into the daughter nuclide. The consistency of this half-life is extremely reliable, and does not depend on any aspect of the environment.
It will be the same everywhere in the universe, and under any set of conditions. And because the isotopes of a given element also have a very reliable natural abundance, which we use to determine atomic mass, it is a relatively straightforward matter to compare some isotopic ratio in a particular geologic material with the naturally occurring ratio in matter which is being formed and freely exchanged with its environment, like the way that carbon-14 is produced by cosmic rays from the sun and maintains a nearly constant concentration in the atmosphere. This comparison allows us to determine how many half-lives have elapsed, and therefore the age of the object.
Each radioisotope has a unique time period over which it is useful for dating, which is related to its half-life. Namely, the parent must have decayed enough to produce a measurable amount of the daughter isotope, but not so much that the parent has almost totally disintegrated. Here are a few of the most commonly used parent-daughter pairs and the ages over which they are useful.
Carbon-14 and nitrogen-14, 300 to 50,000 years. Potassium-40 and argon-40, 100,000 to 4. 3 billion years.
Uranium-238 and lead-206, 1 million to 4. 5 billion years. Potassium-argon dating is used to date rock with potassium-containing minerals, such as biotite and potassium feldspar.
Uranium-lead dating is often used to date the oldest materials on Earth, primarily because these old materials are almost exclusively zircon grains, which take up small amounts of uranium, but do not take up lead, meaning that all the lead which can be found in zircon accumulates by the decay of uranium. This is an important assumption that must be made in order to do some types of radiometric dating, which is that the material being analyzed did not contain any isotopes of the daughter element at the time it was crystallized. However, isochron dating does not require this.
Let’s now go over how the radiometric dating process works. First, a suitable rock and an isotope system must be chosen. Let’s say our hypothetical rock contains biotite as its only source of potassium, so we will use the potassium-argon system.
Geologists must then check the rock’s minerals with a microscope to ensure that the rock has not been hydrothermally altered in any way. The sample is then analyzed by a mass spectrometer to determine the amount of radiogenic argon, which can then be used to calculate the age using the following formula, where 40Art is the current amount of radiogenic argon, 40Art0 is the amount of argon-40 at the time of crystallization, 40Kt0 is the amount of potassium-40 at the time of crystallization, λ is the decay constant, which is 5. 543 x 10-10, and λ_e/λ is the fraction of potassium-40 that decays via electron capture, which is 0.
1048, as potassium-40 can also decay to calcium-40 through beta emission. Next, because argon is not taken up into biotite during crystallization, we can assume that 40Art0 is zero. We can also calculate 40Kt0 simply by knowing the amount of potassium in biotite, which is 4.
49 x 10-4 moles potassium per gram biotite and multiplying it by the fraction of potassium 40 in nature, which is 1. 19 x 10-4. After rearranging the equation we arrive at this, and we can now solve for t.
A rock that contains 5 x 10-10 moles of argon per gram of biotite would have a radiogenic age of 154 million years. There are other isotope pairs, such as rubidium-strontium and uranium-lead, where age is determined by analyzing the relevant isotopes of each mineral of a rock and graphing them. In the case of rubidium-strontium, rubidium-87 breaks down into strontium-87 through negatron decay, another way of saying beta emission.
Here, rubidium-87 is the parent isotope, strontium-87 is the daughter isotope, and strontium-86 is the non-radiogenic isotope of the daughter element. Making a graph with the strontium-87 to 86 ratio on the y-axis and the rubidium-87 to strontium-86 ratio on the x-axis, and plotting the values for the various minerals contained in the rock, creates a straight line called an isochron. Steeper slopes indicate older samples where more decay has occurred over a long period of time.
The exact age can be determined by dividing the slope of the isochron by the decay constant. Furthermore, the y-intercept of the isochron gives the ratio of strontium 87 to 86 at the time of crystallization. So that covers some basic information regarding relative and absolute dating methods, which we can use to determine the age of geologic features, and even the Earth itself.
It is quite astounding that we are able to probe nature to such a sophisticated degree that we are able to get answers to questions that have profound philosophical impact, such as the age of the world we live on, but this is simply a testament to the power of scientific inquiry, and the efforts of those who dedicate themselves to expanding the breadth of scientific knowledge.
