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The Shroud of Turin was found to contain 92 percent of the carbon-14 present in living tissue when tested in 1988, with carbon-14's half-life at 5,730 years. About how old was the shroud's linen at the time of testing?
A70 years
B690 years
C2,865 years
D5,730 years
Answer & Solution
Correct answer: B. 690 years
1. Since 92 percent of carbon-14 remains, N divided by N0 equals 0.92, so N = N0 times e to the power of minus lambda t.
2. Taking the natural logarithm gives ln(0.92) = minus lambda t, or about -0.0834 = minus lambda t.
3. The decay constant is lambda = 0.693 divided by 5,730 years, which is about 1.21 x 10^-4 per year.
4. Solve for t: t = 0.0834 divided by 1.21 x 10^-4.
5. Dividing gives t of about 690 years.
6. 70 years is roughly a tenth of this, and 2,865 or 5,730 years are far too old for only an 8 percent loss of carbon-14.
7. So 690 years is correct.
_Source: OpenStax Physics (CC BY 4.0), Ch 22 "The Atom", section 22.3 Half Life and Radiometric Dating_
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