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 50 % of-life to have 14 C is roughly 5700 age, as well as the fourteen C isotope is just utilized for dating fossils around on the fifty,one hundred thousand yrs old. Fossils more than fifty,100000 decades ount out of 14 C. To possess older fossils, an enthusiastic isotope which have a lengthier 50 % of-lifestyle can be made use of. Like, the radioactive isotope potassium-forty decays so you’re able to argon-40 with a half-life of 1.3 billion years. Most other isotopes commonly used getting relationship become uranium-238 (half-longevity of cuatro.5 mil ages) and you may thorium-232 (half-lives 14.step one million decades).
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