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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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The latest 1 / 2 of-existence to own fourteen C is approximately 5700 many years, as well as the 14 C isotope is only employed for relationship fossils around in the fifty,100000 years old. Fossils avove the age of fifty,100000 decades ount out of 14 C. To own earlier fossils, an isotope that have a longer 1 / 2 of-lifestyle should be utilized. Such as for example, the latest radioactive isotope potassium-40 decays in order to argon-40 that have a half-life of 1.step 3 mil many years. Most other isotopes widely used to have relationships include uranium-238 (half-lifetime of 4.5 million age) and you may thorium-232 (half-lives 14.step one mil age).
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