# Radioactive Decay and Certain Amounts C-14

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• Published : October 29, 2011

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Production of Carbon- 14 (C-14)

The most common isotope of Carbon is C-12. However C-14 can form in the atmosphere as a result of neutrons from cosmic rays colliding with Nitrogen. This removes a proton from the nitrogen, resulting in the formation of C-14 (Image 1). However, C-14 is not a stable isotope and will undergo radioactive decay. C-14 would decay back into N-14 through beta decay. It has a short half life of approximately 5730 years. This means half the initial amount of C-14 would remain in 5730 years with the rest decaying back to nitrogen (Image 2). Since it is radioactive, C-14 would have disappeared from the Earth if it was not for the continuous production of C-14 in the atmosphere.

Carbon and Life

C-14 is able to react with oxygen in order form carbon dioxide. Plants consume carbon dioxide in photosynthesis and release oxygen. This means the plants would have also consumed small amounts of C-14. Other living organisms that consume the plants would also have traces of C-14. Living organisms would have certain amounts C-14 because they are constantly replenishing their supply. However, once the organism dies, it will no longer replenish its supply of C-14. Since C-14 is radioactive, it will decay, and the concentration of C-14 in the dead organism will continue to decrease as time passes by.

Measurement

Since the half life of C-14 is known, the amount of C-14 detected in a dead organism can be compared to the expected amount of C-14 in a living organism to determine the age of the organism.. Using calculus, the following formula to calculate the age of an organism was created:

Where N is the amount of C-14 detected, N0 is the initial amount of C-14, t1/2 is the half life (5730 years), and t is the age of the organism. Since C-14 has a short half life, carbon dating can only determine the age of organisms up to 55,000 years old.

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