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The half-life of radium is 1690 years. If 70 grams are present now, how much will be present in 570 years?

User TelKitty
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1 Answer

25 votes
25 votes

Solution

Given that

Half life is 1690 years.

Let A(t) = amount remaining in t years


\begin{gathered} A(t)=A_0e^(kt) \\ \\ \text{ where }A_{0\text{ }}\text{ is the initial amount} \\ \\ k\text{ is a constant to be determined.} \\ \end{gathered}

SInce A(1690) = (1/2)A0 and A0 = 70


\begin{gathered} \Rightarrow35=70e^(1690k) \\ \\ \Rightarrow(1)/(2)=e^(1690k) \\ \\ \Rightarrow\ln((1)/(2))=1690k \\ \\ \Rightarrow k=(\ln((1)/(2)))/(1690) \\ \\ \Rightarrow k=-0.0004 \end{gathered}

So,


A(t)=70e^(-0.0004t)
\Rightarrow A(570)=70e^(-0.0004(570))\approx55.407\text{ g}

Therefore, the answer is 55.407 g

User Angad Bansode
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