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23 June, 04:26

Suppose you have 100 grams of radioactive plutonium-239 with a half-life of 24,000 years. how many grams of plutonium-239 will remain after

a. 12,000 years

b. 24,000 years

c. 96,000 years?

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Answers (1)
  1. 23 June, 04:33
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    To solve this problem, let us first calculate for the rate constant k using the half life formula:

    t1/2 = ln 2 / k

    where t1/2 = half life period = 24,000 years, therefore k is:

    k = ln 2 / 24,000

    k = 2.89 x 10^-5 / yr

    Now we use the rate equation:

    A = Ao e^ (-k t)

    where,

    A = mass of Plutonium-239 after number of years

    Ao = initial mass of Plutonium-239

    t = number of years

    A. t = 12,000 years, find A

    A = 100g e^ ( - 2.89 x 10^-5 * 12,000)

    A = 70.7 g

    B. t = 24,000 years, find A

    A = 100g e^ ( - 2.89 x 10^-5 * 24,000)

    A = 50 g

    C. t = 96,000 years, find A

    A = 100g e^ ( - 2.89 x 10^-5 * 96,000)

    A = 6.24 g
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