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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 fresh new half of-existence getting fourteen C is roughly 5700 ages, therefore the 14 C isotope is only utilized for matchmaking fossils up to from the fifty,000 years old. Fossils over the age of 50,100000 many years ount away from 14 C. To have old fossils, an isotope having a lengthier half of-lives shall be made use of. Including, the newest radioactive isotope potassium-forty decays so you can argon-forty with a half life of just one.step three billion age. Most other isotopes commonly used to have relationship tend to be uranium-238 (half-lifetime of cuatro.5 mil years) and thorium-232 (half-lives fourteen.step 1 billion decades).

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