Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.

When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is –0.693.

For example, say a fossil is found that has 35% carbon 14 compared to the living sample. We can use a formula for carbon 14 dating to find the answer.

So if we have y = 10^x, then the inverse is log base 10. log base b(1) = 0; that's like saying the natural log of 1 is equal to 0. All of these properties are the same, regardless of whether you're looking at the natural log or the log. If you have an equation like y = a^x, we call a the base and x the exponent. If the base is e, log base e is the same thing as saying the natural log.

So y = 10^x is the same thing as saying log base 10(y) = x.

If you set the percentage of carbon that you have, and you know what this C is, you can calculate how old your item is. I said that the half-life of carbon is 5,730 years.

If the amount of carbon 14 is halved every 5,730 years, it will not take very long to reach an amount that is too small to analyze. This is why it is such a big concern when a nuclear submarine sinks... (By the way, you are mostly Carbon-12, which is not radioactive.Eventually, the salt water will eat through the steel and release the Plutonium (which, as you know, is quite lethal.) They usually talk about either trying to raise the sub or encase it in concrete where it rests. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek.)Scientists use Carbon-14 to make a guess at how old some things are -- things that used to be alive like people, animals, wood and natural cloths. Anyway, they make an estimate of how much Carbon-14 would have been in the thing when it died...Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.So, the fossil is 8,680 years old, meaning the living organism died 8,680 years ago.Archaeology is the systematic study of past human life and culture by the recovery and examination of remaining material evidence, such as graves, buildings, tools, and pottery.When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay.

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