In 8,450 seconds, the number of radioactive nuclei decreases to 1/16 of the number present initially. What is the half-life (in s) of the ma

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In 8,450 seconds, the number of radioactive nuclei decreases to 1/16 of the number present initially. What is the half-life (in s) of the material

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niczorrrr 5 years 2021-08-10T13:54:58+00:00 1 Answers 10 views 0

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  1. diemthu
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    2021-08-10T13:56:36+00:00
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    Answer:

    2113 seconds

    Explanation:

    The general decay equation is given as N = N_0e^{-\lambda t} \\\\, then;

    \dfrac{N}{N_0} = e^{-\lambda t} \\ where;

    N/N_0 is the fraction of the radioactive substance present = 1/16

    \lambda is the decay constant

    t is the time taken for decay to occur = 8,450s

    Before we can find the half life of the material, we need to get the decay constant first.

    Substituting the given values into the formula above, we will have;

    \frac{1}{16} = e^{-\lambda(8450)} \\\\Taking\ ln\ of \both \ sides\\\\ln(\frac{1}{16} ) = ln(e^{-\lambda(8450)}) \\\\\\ln (\frac{1}{16} ) = -8450 \lambda\\\\\lambda = \frac{-2.7726}{-8450}\\ \\\lambda = 0.000328

    Half life f the material is expressed as t_{1/2} = \frac{0.693}{\lambda}

    t_{1/2} = \frac{0.693}{0.000328}

    t_{1/2} = 2,112.8 secs

    Hence, the half life of the material is approximately 2113 seconds

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