13.5.1: Radiocarbon Dating

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Learning Objectives

Identify the age of materials that can be approximately determined using Radiocarbon dating.

Radiometric Dating

Several radioisotopes have half-lives and other properties that make them useful for purposes of “dating” the origin of objects such as archaeological artifacts, formerly living organisms, or geological formations. The radioactivity of carbon-14 provides a method for dating objects that were a part of a living organism. This method of radiometric dating, which is also called radiocarbon dating or carbon-14 dating, is accurate for dating carbon-containing substances that are up to about 30,000 years old, and can provide reasonably accurate dates up to a maximum of about 50,000 years old.

Naturally occurring carbon consists of three isotopes: ${}_{6}^{12}C$

, which constitutes about 99% of the carbon on earth; ${}_{6}^{13}C$ , about 1% of the total; and trace amounts of ${}_{6}^{14}C$

. Carbon-14 forms in the upper atmosphere by the reaction of nitrogen atoms with neutrons from cosmic rays in space:

N 714 + n 01 ⟶ C 614 + H 11

All isotopes of carbon react with oxygen to produce CO₂ molecules. The ratio of ${}_{6}^{14}{CO}_{2}$

to ${}_{6}^{12}{CO}_{2}$ depends on the ratio of ${}_{6}^{14}{CO}$ to ${}_{6}^{12}{CO}$ in the atmosphere. The natural abundance of ${}_{6}^{14}{CO}$ in the atmosphere is approximately 1 part per trillion; until recently, this has generally been constant over time, as seen is gas samples found trapped in ice. The incorporation of ${}_{6}^{14}C {}_{6}^{14}{CO}_{2}$ and ${}_{6}^{12}{CO}_{2}$ into plants is a regular part of the photosynthesis process, which means that the ${}_{6}^{14}C : {}_{6}^{12}C$ ratio found in a living plant is the same as the ${}_{6}^{14}C : {}_{6}^{12}C$ ratio in the atmosphere. But when the plant dies, it no longer traps carbon through photosynthesis. Because ${}_{6}^{12}C$

is a stable isotope and does not undergo radioactive decay, its concentration in the plant does not change. However, carbon-14 decays by β emission with a half-life of 5730 years:

C 614 ⟶ N 714 + e - 1 0

Thus, the ${}_{6}^{14}C : {}_{6}^{12}C$

ratio gradually decreases after the plant dies. The decrease in the ratio with time provides a measure of the time that has elapsed since the death of the plant (or other organism that ate the plant). Figure $14.3. 2$

visually depicts this process.

A diagram shows a cow standing on the ground next to a tree. In the upper left of the diagram, where the sky is represented, a single white sphere is shown and is connected by a downward-facing arrow to a larger sphere composed of green and white spheres that is labeled “superscript 14, subscript 7, N.” This structure is connected to three other structures by a right-facing arrow. Each of the three it points to are composed of green and white spheres and all have arrows pointing from them to the ground. The first of these is labeled “Trace, superscript 14, subscript 6, C,” the second is labeled “1 percent, superscript 13, subscript 6, C” and the last is labeled “99 percent, superscript 12, subscript 6, C.” Two downward-facing arrows that merge into one arrow lead from the cow and tree to the ground and are labeled “organism dies” and “superscript 14, subscript 6, C, decay begins.” A right-facing arrow labeled on top as “Decay” and on bottom as “Time” leads from this to a label of “superscript 14, subscript 6, C, backslash, superscript 12, subscript 6, C, ratio decreased.” Near the top of the tree is a downward facing arrow with the label “superscript 14, subscript 6, C, backslash, superscript 12, subscript 6, C, ratio is constant in living organisms” that leads to the last of the lower statements. — Figure $14.3. 2$

: Along with stable carbon-12, radioactive carbon-14 is taken in by plants and animals, and remains at a constant level within them while they are alive. After death, the C-14 decays and the C-14:C-12 ratio in the remains decreases. Comparing this ratio to the C-14:C-12 ratio in living organisms allows us to determine how long ago the organism lived (and died). (CC BY 4.0; OpenStax)

For example, with the half-life of ${}_{6}^{14}C$

being 5730 years, if the ${}_{6}^{14}C : {}_{6}^{12}C$ ratio in a wooden object found in an archaeological dig is half what it is in a living tree, this indicates that the wooden object is 5730 years old. Highly accurate determinations of ${}_{6}^{14}C : {}_{6}^{12}C$ ratios can be obtained from very small samples (as little as a milligram) by the use of a mass spectrometer.

When we speak of the element Carbon, we most often refer to the most naturally abundant stable isotope ¹²C. Although ¹²C is definitely essential to life, its unstable sister isotope ¹⁴C has become of extreme importance to the science world. Radiocarbon dating is the process of determining the age of a sample by examining the amount of ¹⁴C remaining against its known half-life, 5,730 years. The reason this process works is because when organisms are alive, they are constantly replenishing their ¹⁴C supply through respiration, providing them with a constant amount of the isotope. However, when an organism ceases to exist, it no longer takes in carbon from its environment and the unstable ¹⁴C isotope begins to decay. From this science, we are able to approximate the date at which the organism lived on Earth. Radiocarbon dating is used in many fields to learn information about the past conditions of organisms and the environments present on Earth.

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