Methods of Dating the Earth Part 2: Absolute Dating (Radiometric Dating)

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.