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My teacher taught me that during carbon dating a fresh live sample is obtained, the activity of carbon-14 in the sample is determined, and then the level of activity is compared with that of the dead sample. From this, the number of years the dead sample has spent in the soil (dead) can be obtained.

I am confused by this explanation, could someone elaborate/clarify?

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While we are alive we continuously exchange carbon with the environment. We eat food containing carbon, metabolise it and exhale carbon dioxide containing carbon. So most of our body tissue maintains the same ${}^{12}$C to ${}^{14}$C ratio as the environment around us.

However when we die we no longer eat, metabolise and exhale so the carbon ratio in our bodies is frozen in. From the moment of death onwards the ratio of ${}^{12}$C to ${}^{14}$C increases with time as the ${}^{14}$C decays.

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    $\begingroup$ This doesn't explain why the carbon 14 to carbon 12 ratio doesn't also decay in the environment. It should decay the same way as in the (dead or alive) body. $\endgroup$ – freecharly Dec 30 '16 at 18:48
  • $\begingroup$ @freecharly Carbon-14 is continuously produced by interactions between cosmic rays and the atmosphere --- mostly $\rm ^{14}N + p \to n + {}^{14}C$. $\endgroup$ – rob Jan 10 '17 at 20:17
  • $\begingroup$ @ rob - Thank you. That's what I pointed out in my answer below. $\endgroup$ – freecharly Jan 10 '17 at 22:25
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The principle of the carbon-14 dating is based on the fact that the constant irradiation of cosmic rays transmutes nitrogen in the atmosphere into the radioactive isotope carbon-14. Thus a stationary ratio of carbon-14 to carbon-12 is maintained in the atmosphere. When a living being (plant, animal, human) dies, there is no more exchange of carbon and thus carbon-14 of this being with the atmosphere. Thus, due to the radioactive decay of carbon-14, the ratio of carbon-14 to carbon-12 decreases beginning at the time of death. Therefore, the measurement of this ratio enables the dating of the death and thus historical age of the object investigated.

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