You find a piece of cloth painted with organic dye. By analyzing the dye, you find that only 83 % of the carbon-14 originally in the dye remains. When was the cloth painted?

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  1. After 1 half-life 50% should be gone.
    only 17% is gone, so this is just a portion of 1 half-life.

    17/50 = .34 half-life

    5730 times .34 should be your answer

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  2. Nope.

    take ln of each side.

    t= -5730*ln(.83)/.693=1541years

    which is about 400 years different than the first answer.

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  3. It might be instructive to note that ALL radio decay is 1st order decay. Such is the value of the 1st order decay equation C(remaining) = C(initial)e^(-kt) where k = rate constant = 0.693/(Half-Life). In this case Half-Life of C-14 = 5730 Years => k = (0.693/5730)yrs^-1. Using the classic 1st order time of decay equation = [(ln(remaining/initial)]/-k = ln(83%/100%)/-(1.21x10^-4) = 1540 yrs.

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