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For example, suppose you have N0 grams of a radioactive isotope that has a half-life of t * years. Then we know that after one half-life (or t * years later), you will have
Returning to our example of carbon, knowing that the half-life of 14 C is 5700 years, we can use this to find the constant, k. That is when t = 5700, there is half the initial amount of 14 C. Of course the initial amount of 14 C is the amount of 14 C when t = 0 , or N0 (i.e. N(0) = N0e k?0 = N0e 0 = N0). Thus, we can write:
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Brand new half of-existence getting 14 C is approximately 5700 years, and the fourteen C isotope is just used in matchmaking fossils up to about 50,000 years of age. Fossils avove the age of fifty,000 decades ount regarding fourteen C. To possess old fossils, an isotope with an extended 1 / 2 of-lives will likely be utilized. Such as, brand new radioactive isotope potassium-forty decays in order to argon-forty that have a half-life of just one.step three mil age. Other isotopes popular to possess matchmaking were uranium-238 (half-lifetime of 4.5 billion age) and thorium-232 (half-lives fourteen.step 1 million years).
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