# Carbon-14 Dating. or, How Old Are Those M&Ms? Number of Undecayed M&Ms

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1 BRSP - 15 Page 1 Carbon-14 Dating or, How Old Are Those M&Ms? One of the tools available to scientists who study ancient climates is called carbon-14 dating (also known as carbon dating or radiocarbon dating). This method is used, within limits, to determine the ages of certain types of objects. Carbon dating makes use of the fact that some atoms radioactive atoms change over time into other types of atoms in a natural process known as radioactive decay. The decay of radioactive atoms occurs in a predictable way: After a length of time has elapsed, exactly one-half of the original atoms will have changed, leaving the other half unchanged. The length of time it takes for half of the atoms to decay is called a half-life. Each type of radioactive element has a distinct half-life different from all other elements. The half-life of a radioactive element does not vary. Warm-Up Activity Before reading more about carbon-14 dating, do the following activity to see how the concept of halflife may be described mathematically. 1. Put exactly M&M candies into a paper cup (do not eat them yet you will need all!). The M&Ms represent carbon-14 atoms before decay. 2. Shake the cup and empty it onto a clean sheet of paper. For this activity, each shake of the cup (each run) represents one half-life. 3. Remove the M&Ms that have the label up these are the atoms that have decayed. (Now you may eat the removed M&Ms!) 4. Record the number of remaining, undecayed, M&Ms in the table below under Repeat this procedure with several more runs until all M&Ms are gone or until there is only one left. 6. Graph each of the data points and connect them to form a line graph. 7. Obtain the class average for each run and plot the data to make a second line on the graph. 8. Finally, calculate the theoretical half-life values for all runs and graph them as a third line. The theoretical values are based on the assumption that label-side-up and label-side-down are equally probable for example, the theoretical value is 50 after the first run. 9. Label the three lines on the graph. Number of Undecayed M&Ms Start Individual or Group Value Class Average Theoretical Value

2 BRSP - 15 Page 2 Graph of M&M Decay Number of Undecayed M&Ms Number of s (Half-Lives) In mathematics, a smooth, declining curve of the type just drawn is called, not coincidentally, exponential decay. Discussion points: Which graph line the individual or class average most closely follows the theoretical line? Why? The declining number of M&Ms after each succeeding run is like the radioactive decay of atoms after each half-life has passed. Eventually, the number of remaining atoms from the original quantity approaches zero, as almost all of the atoms have decayed into a different atomic form. Why Carbon-14? Carbon dating is performed on objects containing bits of organic matter, carbon-based substances that were once included in the bodies of living plants and animals. Not all carbon atoms are alike. Approximately 99 percent of carbon atoms have atomic nuclei with six protons and six electrons, giving them an atomic mass of 12. About one percent of carbon atoms have an extra neutron in the nucleus, giving them an atomic mass of 13. A very small number of carbon atoms about one in every trillion have two additional neutrons, giving them an atomic mass of 14. These different types of carbon atoms are called isotopes (see figure on next page). The carbon-14 atoms are unstable and will disappear, or decay, on their own in time. This fact is central to understanding how carbon dating is used to establish the age of an object.

3 BRSP - 15 Page 3 carbon 12 stable carbon 13 stable carbon 14 unstable (radioactive) Because all living things are made from organic molecules, they must have a carbon source in order to exist. For most organisms, that source is carbon dioxide (CO 2) in the atmosphere. The carbon atoms in the atmosphere include the three isotopes in the proportions stated above. The same proportions are found in the organisms that obtain their carbon from the atmosphere. Those proportions will stay the same in their bodies for as long as they are living, because the carbon in living organisms is continuously being replenished. When an organism dies, however, the carbon is no longer replaced. It remains there until it is eventually returned to the ecosystem through decomposition processes. The radioactive carbon-14 in the dead organism decays in a known way, similar to the decay curve for M&Ms. Imagine a pollen grain that is picked up by the wind and carried aloft. After traveling hundreds of miles, the pollen grain settles onto a glacier and becomes buried under many annual snowfalls. Thousands of years later, a geologist removes an ice core from the glacier and finds that same pollen grain in his sample of ice. Can he determine the age of the pollen grain? If so, he will also know how old that part of the glacier is. Using carbon dating, the geologist can closely estimate the age of the sample. By measuring the ratio of carbon-14 to all carbon atoms in the pollen grain, he will know how much carbon-14 decay has occurred. The extent of decay will reveal the age of the pollen grain. Shallow ice core drilling, Greenland Radioactive decay of carbon-14

4 BRSP - 15 Page 4 Graphing the Decay of Carbon-14 Knowing that the half-life of carbon-14 is 5,730 years, it is easy to construct a decay curve like the one for M&Ms. Complete the following table and make a line graph of the data on the chart provided. The result should be a smooth, curving line through all points. Decay of Carbon-14 Years from Present 0 5,730 11,460 17,190 22,920 28,650 34,380 40,110 45,840 51,570 Percent of Original C14 Remaining Decay of Carbon Percent of Original Carbon ,000 20,000 30,000 40,000 50,000 Years from Present Carbon dating is generally useful for dating objects up to about 50,000 years old. Why is this method limited for objects of greater age? Fortunately, for scientists who need larger measuring sticks, there exist other elements whose radioactive isotopes have half-lives greater than that of carbon-14 and can be used in a similar manner as dating tools.

7 BRSP - 15 Page 7 Visit these websites for more information about radiocarbon dating: Extension Activity Many students will be familiar the water cycle (hydrologic cycle). Some may also have knowledge of the carbon, nitrogen, and oxygen cycles. It is one of the most fundamental principles of environmental/earth science that these substances are continuously moving, in various forms, within and between the atmosphere, biosphere, and geosphere. The science of radiocarbon dating is directly dependent on the transfer of carbon through the carbon cycle. However, the carbon cycle is so interconnected with the movement of oxygen that a more complete picture is presented by describing the carbon-oxygen cycle. Students can learn about the carbon-oxygen cycle from a wide array of print materials and online resources. One way to demonstrate their knowledge of this subject is to create a poster of the carbon-oxygen cycle. A good version of the poster assignment (including written component) can be found at the website listed below. This website also provides a list of suggested links for students reference.

8 BRSP - 15 Page 8 ANSWER KEY Decay of Carbon-14 Years from Present 0 5,730 11,460 17,190 22,920 28,650 34,380 40,110 45,840 51,570 Percent of Original C14 Remaining Decay of Carbon Percent of Original Carbon ,000 20,000 30,000 40,000 50,000 Years from Present

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