6 a 100 sample of Au – 198 Au 198 be? Decays to 3.125 g in 13.5 days, what would the half-life of au198 be?

Question

6 a 100 sample of Au – 198 Au 198 be? Decays to 3.125 g in 13.5 days, what would the half-life of au198 be?

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Adela 6 months 2021-07-29T16:24:01+00:00 1 Answers 4 views 0

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    2021-07-29T16:25:06+00:00

    Answer:

    Half-life = 2.7 days

    Explanation:

    The radioactive decay of an isotope follows the equation:

    Ln[A] = -kt + ln[A]₀

    Where [A] could be taken as the amount of A after t time, k is decay constant, [A]₀ initial amount of A.

    Replacing to solve k:

    Ln[3.125g] = -k*13.5days + ln[100g]

    -3.465736 = -k*13.5days

    k = 0.2567days⁻¹

    Half-life is:

    half-life = ln2 / k

    Half-life = 2.7 days

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