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The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.
It has been determined that the rate of radioactive decay is first order.
We can apply our knowledge of first order kinetics to radioactive decay to determine rate constants, original and remaining amounts of radioisotopes, half-lives of the radioisotopes, and apply this knowledge to the dating of archeological artifacts through a process known as carbon-14 dating.
In this equation, the units of measure for N and No can be in grams, atoms, or moles.
It does not matter as long as they are like measures.