If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round t

Question

If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.

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Nick 7 months 2021-07-20T21:15:05+00:00 1 Answers 4 views 0

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    2021-07-20T21:16:38+00:00

    Answer: 26.4\ \text{days}

    Step-by-step explanation:

    Given

    Half life of radioactive substance is T_{\frac{1}{2}}=20\ \text{days}

    Initial amount A_o=2\ \text{days}

    Amount left at any time is given by

    \Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}

    It takes 26.4 days to reach 2 gm.

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