# astronomy

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

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2. Nope.

.83=e^(-.693*t/5730)
take ln of each side.
ln(.83)=-.693t/5730

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

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bobpursley
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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