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Question

Scientists think that Earth once had naturally existing plutonium-239239. Suppose Earth had 1010 trillion tons of Pu239\mathrm{Pu}-239 when it formed. Given plutonium's half-life of 24,00024,000 years and Earth's current age of 4.64.6 billion years, how much would remain today? Use your answer to explain why plutonium is not found naturally on Earth today.

Solution

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Answered 1 year ago
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The amount of plutonium after a certain time can be calculated using the expression

new value=initial value(12)tThalf=101012(12)4.610924,000=3.83851057,685 tons\begin{align*} \text{new value}&=\text{initial value}\cdot\left(\dfrac12\right)^{\frac{t}{T_\text{half}}}\\ &=10\cdot10^{12}\cdot\left(\dfrac12\right)^{\frac{4.6\cdot10^9}{24,000}}\\ &=3.8385\cdot10^{-57,685}\ \text{tons} \end{align*}

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