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6 September, 06:43

How long will it take for 20% of the u-238 atoms in a sample of u-238 to decay?

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  1. 6 September, 08:09
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    Answer is: it takes 1,448 billion years.

    The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration.

    c₀ - initial concentration of U-238.

    c - concentration of U-238 remaining at time.

    t = 4,5 ·10⁹ y.

    First calculate the radioactive decay rate constant λ:

    λ = 0,693 : t = 0,693 : 4,5·10⁹ y = 1,54·10⁻¹⁰ 1/y.

    ln (c/c₀) = - λ·t₁.

    ln (0,8/1) = - 1,54·10⁻¹⁰ 1/y · t₁.

    t₁ = 1,448·10⁹ y.
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