An investigator collects a sample of a radioactive isotope with an activity of 490,000 Bq.48 hours later, the activity is 110,000 Bq. Part A

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An investigator collects a sample of a radioactive isotope with an activity of 490,000 Bq.48 hours later, the activity is 110,000 Bq. Part A For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution What is the half-life of the sample?

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Latifah 2 months 2021-07-24T01:41:04+00:00 1 Answers 26 views 0

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    2021-07-24T01:42:12+00:00

    Answer:

    The correct answer is “22.27 hours“.

    Explanation:

    Given that:

    Radioactive isotope activity,

    = 490,000 Bq

    Activity,

    = 110,000 Bq

    Time,

    = 48 hours

    As we know,

    A = A_0 e^{- \lambda t}

    or,

    \frac{A}{A_0}=e^{-\lambda t}

    By taking “ln”, we get

    ln \frac{A}{A_0}=- \lambda t

    By substituting the values, we get

    -ln \frac{110000}{490000} = -48 \lambda

    ⇒    -1.4939=-48 \lambda

                     \lambda = 0.031122

    As,

    \lambda = \frac{ln_2}{\frac{T}{2} }

    then,

    \frac{ln_2}{T_ \frac{1}{2} } =0.031122

    T_\frac{1}{2}=\frac{ln_2}{0.031122}

             =22.27 \ hours  

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