14.6: Numeric Dating

Numeric Dating

Unlike relative dating methods, numeric (or absolute) dating methods provide specific numeric ages for rock layers and help measure the rates at which geologic processes operate. There are numerous scientific techniques to determine a numeric age. For example, we might date trees by counting the number of annual growth rings, using a science called dendrochronology Links to an external site.. For geoscientists, however, the most used (and useful!) numeric dating technique is radiometric or isotopic dating Links to an external site.. For this technique, radiometric isotopes are measured in rock samples. An isotope Links to an external site. is an atom of an element with a different number of neutrons, and therefore different atomic weight; all elements on the periodic table have isotopes. If an atom has too many or too few neutrons in its nucleus, it becomes unstable and breaks down over time, through a process called radioactive decay Links to an external site..

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⚒️Can You Dig It?

CHEMISTRY THROWBACK: Atoms Links to an external site. are made of three particles: protons Links to an external site., electrons Links to an external site., and neutrons Links to an external site.. All three of these particles are important to geology. The number of protons defines an element, the number of electrons controls how that element bonds to make compounds, and the number of neutrons changes the atomic weight of an element.

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The process of radioactive decay involves the emission of particles from a radioactive isotope – the parent isotope Links to an external site. – until it loses enough neutrons, electrons, and protons until it changes into another, more stable, element – the daughter isotope Links to an external site.. Scientists can measure the radioactivity of an isotope in the lab and calculate its rate of decay. Though the rate of decay of different isotopes can vary from milliseconds to billions of years, all radiometric isotopes decay in a predictable way.

Radiometric decay follows a distinct curve that is defined by a radiometric isotope’s half-life. The half-life Links to an external site. is defined as the amount of time it takes for half of the atoms of the radiometric parent isotope to decay to the daughter isotope. The half-life is independent of the number of atoms in a material at a given time; because of this, it takes the same amount of time to go from 100% of the parent isotope remaining to 50%, as it does to go from 50% of the parent isotope remaining to 25% (Figure 14.16).

If the length of the half-life for a radiometric isotope is known, and we measure the amount of parent and daughter isotope in a rock, we can then calculate the age of the rock. Given the shape of the decay curve, a material never runs out of the parent isotope completely; however, after around 10-15 half-lives the amount of the parent isotope left is so small that we are unable to effectively measure it. There are several different radiometric isotopes that are commonly used in absolute dating. Each of these systems has different uses within geology, because they require different materials and can date objects within different time frames.

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Carbon-14 dating, which may sound familiar to you, is actually of limited use within geology. Carbon-14 (the unstable parent isotope) is found in organic material like bone, tissue, plants, and fiber. This isotope is found naturally in small amounts in the atmosphere within CO₂ and is incorporated into plants during photosynthesis and then permeates through the food chain. You currently have carbon-14 in your body that is decaying to nitrogen-14 (daughter isotope), but you replace it whenever you eat. When an animal stops eating or a plant stops photosynthesizing (i.e. when they die), the radioactive carbon starts to decay without being replaced and can be easily measured. Carbon-14 has a very short half-life, only 5730 years, so it can only be used to date materials up to approximately 60,000 years in age. Given that the age of the Earth is 4.54 billion years, carbon-14 is not useful for dating materials from most of Earth’s history.

For geology, we typically require isotopes with much longer half-lives (Table 14.2). Uranium dating involves a complex system of multiple isotopes that decay through a chain reaction until it reaches non-radiogenic lead. Uranium can be found naturally in many igneous rocks, notably the ubiquitous continental rock granite, but in very small amounts. Uranium-238 decays to lead-206, which is also found naturally in many different places; this can make it challenging to differentiate between lead formed from radiometric decay and lead found naturally in the environment. 

Table 14.2: Common half-life pairs used in the geosciences. (CC-BY 4.0, Chloe Branciforte)

Parent Isotope	Daughter Isotope	Half-life	Dating Range	Comments
Potassium-40	Argon-40	1.3 Ga	10 ka-4.57 Ga	Widely applicable because most rocks have some potassium. Found in Muscovite, Biotite, Hornblende, and whole volcanic rock.
Uranium-238	Lead-206	4.5 Ga	1 Ma-4.57 Ga	The rock must have uranium-bearing minerals. Found in Zircon and Uraninite.
Rubidium-87	Strontium-87	47 Ga	10 Ma-4.57 Ga	Less precision than other methods at old dates. Found in Muscovite, Biotite, Potassium feldspar, whole igneous or metamorphic rock.
Carbon-14	Nitrogen-14	5,730 years	100 to 60,000 years	Found in wood, charcoal, peat, bone & tissue, shell or other calcium carbonate, groundwater, ocean water, glacier ice. Can be applied to young sediments.

The mineral zircon Links to an external site. (Figure 14.17) solves both issues, by concentrating uranium and excluding lead from its mineral structure. Therefore, we use Uranium dating on zircons found within igneous rocks (such as volcanic ash or rocks formed deep in the earth). Uranium has a very long half-life of 4.57 billion years, which is more than long enough to date most rocks on Earth.

Potassium-Argon dating Links to an external site. is also a useful method of dating rocks. Potassium decays into two separate daughter isotopes, argon and calcium. Geologists will measure the amount of argon, a noble gas Links to an external site., in minerals because, unlike calcium, it is rare and does not normally bond with other elements. Therefore, we can be sure that any argon within a mineral is from the decay of potassium. The use of argon also has its drawbacks; for instance, a gas can easily escape from a rock and, therefore, special care needs to be taken in the lab to prevent this. This system works well when there are multiple materials to examine that contain abundant potassium, like the rock granite that is full of the potassium-rich pink feldspars. The half-life of potassium is 1.3 billion years, so, like uranium, it is most useful for dating older rocks.

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With all these methods there is still the chance for error such that it is best to think of any particular radiometric date as a scientific hypothesis that needs to be further tested. Typically, numerical dates are reported with a +/- error bar. Error can come from the inclusion or loss of parent or daughter isotopes in the rock following its formation. This can happen for several reasons, most commonly because of heat and pressure (metamorphism). There are ways to correct for these issues that allow scientists to date both the rock and the metamorphic event as long as the geologic history is known. Improvements in technology continue to provide geologists with more precise instrumentation, resulting in more accurate numerical ages. This means every few years a new Geologic Time Scale is produced to accurately reflect ongoing research.  This is the most recent timescale available from The Geological Society of America Links to an external site.. As you examine the timescale, it might be useful to refer to common unit terminology for isotopic dating (Table 14.3).

Table 14.3: Common unit terminology for isotopic dating.

Units (used to indicate time before present)	Latin meaning	Units (used to indicate duration)	"Time"
Ga	Giga annum	Gya, Gy, Bya, Byr, By	billion years
Ma	Mega annum	Mya, Myr, My	million years
ka	kilo annum	kya, kyr, ky	thousand years

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It is improbable to find a rock that contains the exact number of remaining parent isotopes that falls exactly on one of the half-lives. In most cases, we need to use a simple formula to calculate the age of a rock using the length of the half-life and the amount of parent remaining. The formula is:

$Age=-\left(\frac{t\frac{1}{2}}{0.693}\right)\ln\left(p\right)$

$t\frac{1}{2}$ = The length of the half-life in years

$p$  = The amount of the parent remaining in decimal form. For example, if there is 50% of the parent remaining it would equal 0.5.

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Let’s work an example using the above equation; we can be sure we are using the equation correctly because we will already know the answer to in advance. Say you have a sample of bone that has 25% of the Carbon-14 (half-life= 5,730 years) remaining; how old is the sample? We can answer this question in two ways:

1. We know that if there is 25% remaining, two half-lives have passed and since each half-life represents 5730 years, the bone would be 11,460 years old.
2. We could use the above equation and insert both the length of the half- life and the amount of the parent remaining:

$Age=-\left(\frac{5730}{0.693}\right)\ln\left(0.25\right)$

To solve the equation, take the Natural Log (ln) of 0.25 and multiply by the term in the parentheses (make sure to include the negative sign). If you do this, you should get 11,460 years as well.

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