If carbon‑14 has a half-life of 5730 years, what is the age of the plant fossil in years?

While exploring a coal mine, scientists found plant fossils which had been preserved by an earthquake in the ceiling of the mine. Samples taken from one of the fossils had carbon‑14 activities of 20.0 counts/min. A reference sample of the same size from a plant alive today has a carbon-14 activity of 160.0 counts/min.

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  • Ash
    Lv 7
    2 months ago
    Favorite Answer

    N(t) = Nₒ(½)^(t / t½) .... where t½ = half life

    20.0 = 160.0(½)^(t / 5730)

    ⅛ = (½)^(t / 5730)

    ln(⅛) = ln (½)^(t / 5730)

    ln(⅛) = (t/5730) ln (½)

    t = 5730 ln(⅛)  / ln (½)

    t = 17190 years  ←  age of the plant

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