# Mathematics of carbon dating Intim macag

So this is just an ordinary beta decay process and this carbon fourteen's half life is way way way too short for any carbon to just kind of exist naturally in the atmosphere, you'd think, not quite right. So that mean that 1.3 times 10 to the -12 carbon 14 atoms, exist for each and every carbon 12 atom in nature. So you'd think that if you got this 1.3 times 10 to the -12 carbon 14 atoms for each carbon 12 atom at some time, well then 5700 years later, half of the carbon 14 will have decayed. But in fact what happens is, cosmic rays from the sun interact with the upper atmosphere and they actually create carbon 14, at this rate so that in equilibrium, 1.3 times 10 to the -12 carbon 14 atoms will exist for every carbon 12 atom. It's no longer replenishing its carbon 14 supply. This is our standard radioactive decay formula, always works.

Carbon dating uses an unstable isotope of carbon to find the date of dead substances.

After the second half-life, one-half of the remaining one-half carbon-14 atoms will remain, or one-fourth. The fern therefore died three half-lives of carbon-14 ago: 3 × 5,730 years is 17,190 years.

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The general technique for dating matter using radioactivity is called radiometric dating.

Besides carbon-14, a number of other radioactive isotopes are used for dating.

This technique allows geologists to explore geologic times because the half-life of uranium-238 is 4.5 billion years.