Cesium-137 is part of the nuclear waste produced by uranium-235 fission. The half-life of cesium-137 is 30.2 years. How much time is require

Question

Cesium-137 is part of the nuclear waste produced by uranium-235 fission. The half-life of cesium-137 is 30.2 years. How much time is required for the activity of a sample of cesium-137 to fall to 9.32 percent of its original value

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Ben Gia 1 year 2021-07-23T11:44:05+00:00 1 Answers 17 views 0

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  1. Amity
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    2021-07-23T11:45:56+00:00
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    Answer:

    t(9.32% remaining) = 203 yrs (3 sig. figs.)

    Explanation:

    All radioactive decay follows a 1st order decay profile. This is defined by the expression …

    A =A₀e^-k·t

    A = final activity = 9.32%

    A₀ = initial activity = 100%

    e = base of natural logs

    k = rate constant = 0.693/t(1/2) = (0.693/30.2) yrs⁻¹ = 0.023 yrs⁻¹

    t = time of decay = ln(A/A₀)/-k = ln(9.32%/100%)/-0.023 yrs⁻¹

     = 203.286637 yrs (calc. ans.)

     ≅ 203 yrs (3 sig. figs.)

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