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# Application: Radiocarbon Dating

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 the 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 were living on Earth. Radiocarbon dating is used in many fields to learn information about the past conditions of organisms and the environments present on Earth.

### History of Radiocarbon Dating

Before Radiocarbon dating was able to be discovered, someone had to find the existence of the 14C isotope. In 1940 Martin Kamen and Sam Ruben at the University of California, Berkeley Radiation Laboratory did just that. They found a form, isotope, of Carbon that contained 8 neutrons and 6 protons. Using this finding Willard Libby and his team at the University of Chicago proposed that Carbon-14 was unstable and underwent a total of 14 disintegrations per minute per gram. Using this hypothesis, the initial half-life he determined was 5568 give or take 30 years. The accuracy of this proposal was proven by dating a piece of wood from an Ancient Egyptian barge, of whose age was already known. From that point on, scientist have used these techniques to examine fossils, rocks, and ocean currents and determine age and event timing. Throughout the years measurement tools have become more technologically advanced allowing researchers to be more precise and we now use what is known as the Cambridge half-life of 5730+/- 40 years for Carbon-14. Although it may be seen as outdated, many labs still use Libby's half-life in order to stay consistent in publications and calculations within the laboratory. From the discovery of Carbon-14 to radiocarbon dating of fossils, we can see what an essential role Carbon has played and continues to play in our lives today.

### Nuclear Chemistry of Radiocarbon Dating

The entire process of Radiocarbon dating depends on the decay of Carbon-14. This process begins when an organism is no longer able to exchange Carbon with their environment. Carbon-14 is first formed when cosmic rays in the atmosphere allow for excess neutrons to be produced, which then react with Nitrogen to produce a constantly replenishing supply of Carbon-14 to exchange with organisms.

$\ce { ^1n + ^{14}N \rightarrow ^{14}C + ^1H}$

The process Nitrogen or Carbon Cycle comes full circle when Carbon-14 begins to decay by beta emission. The Carbon reproduces Nitrogen-14 along with an electron and anti-neutrino.

$\ce{ ^{14}C -> ^{14}N + e^-} + \mu_e$

photo from: razd.evcforum.net/Age_Dating.htm

Since we can determine the amount of an isotopic element that remains after a specific period of time, we can conversely determine the time over which a specific sample has been decaying once we know the rate constant for that element. This is the basis of carbon dating. Carbon dating is a process whereby the age of a material that contains carbon can be determined by comparing the decay rate of that material with that of living material.

Carbon-14 has a half life ($$t_{1/2}$$) of $$5.73 \times 10^3$$ years to decay to nitrogen-14 by the loss of a $$\beta$$ particle.

$\ce{^{14}_6C \rightarrow ^{14}_7N + ^0_{-1}e^-}$

Using Equation 1,

$k = \dfrac{0.693}{5.73 \times 10^3} = 1.21 \times 10^{-4} \text{year}^{-1}$

Example 1: Dead Sea Scrolls
n 1947 samples of the Dead Sea Scrolls were analyzed by carbon dating. It was found that the carbon-14 present had an activity (rate of decay) of d/min.g (where d = disintegration). In contrast, living material exhibit an activity of 14 d/min.g. Thus, using Equation 2,

$\ln \dfrac{14}{11} = (1.21 \times 10^{-4}) t$

Thus,

$t= \dfrac{\ln 1.272}{1.21 \times 10^{-4}} = 2 \times 10^3 \text{years}$

From the measurement performed in 1947 the Dead Sea Scrolls were determined to be 2000 years old giving them a date of 53 BC, and confirming their authenticity. This discovery is in contrast to the carbon dating results for the Turin Shroud that was supposed to have wrapped Jesus’ body. Carbon dating has shown that the cloth was made between 1260 and 1390 AD. Thus, the Turin Shroud was made over a thousand years after the death of Jesus.

### Applications in Modern Science

Radiocarbon dating is used in multiple science fields. When any fossil is found, scientists want to know how long ago the organism that it belonged to roamed the Earth. They take the sample back to the lab and determine age by either counting Carbon-14 molecules or using Accelerator Mass Spectrometry. This allows scientist to put together a timeline helping us to better understand the organisms present on Earth at given time periods and the way they may have evolved. Geologist also use radiocarbon dating in order to determine the age of rocks, along with the age and the distributions of others around the same age it makes it much easier to understand plate tectonics and the shifts that took place. Oceanographers also use the measurements of Carbon-14 present in one area of the water to others in order to estimate future and explain past water currents. Radiocarbon dating allows us to make discoveries of past environments on Earth, making it easier for us to understand our origins, courses of evolution, and events that may have shaped the world and made the atmosphere we live in what it is today.

### References

1. Hua, Quan. "Radiocarbon: A Chronological Tool for the Recent Past." Quaternary Geochronology4.5(2009):378-390. Science Direct. Web. 22 Nov. 2009.
2. Petrucci, Raplh H.General Chemistry: Principles and Modern Applications 9th Ed. New Jersey: Pearson Education Inc. 2007.
3. "Radio Carbon Dating." BBC- Homepage. 25 Oct. 2001. Web. 22 Nov. 2009. http://www.bbc.co.uk.
4. Willis, E.H., H. Tauber, and K. O. Munnich. "Variations in the Atmospheric Radiocarbon Concentration Over the Past 1300 Years." American Journal of Science Radiocarbon Supplement 2(1960) 1-4. Print.

### Problems

1. If when a hippopotamus was breathing there was a total of 25 grams of Carbon-14, how many grams will remain 5730 years after he is laid to rest? 12.5 grams, because one half life has occurred.
2. How many grams of Carbon-14 will be present in the hippos remains after 3 half-lives have passed? 3.125 grams of Carbon-14 will remain after 3 half lives.

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17:03, 26 Apr 2014

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