Radiocarbon measurements made in 1988 on the shroud of turin showed a decay rate of 14.2 disintegrations/min per gram of carbon. this is in comparison to the decay rate in the then current living organisms of 15.3 disintegrations/min per gram of carbon. given a half-life of 5730 years for carbon-14, what year is the artifact from?

Question

Chemistry

Louis Guerra

11 September, 17:22

Radiocarbon measurements made in 1988 on the shroud of turin showed a decay rate of 14.2 disintegrations/min per gram of carbon. this is in comparison to the decay rate in the then current living organisms of 15.3 disintegrations/min per gram of carbon. given a half-life of 5730 years for carbon-14, what year is the artifact from?

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Adolfo Leonard · Answer 1

We may use the equation:

A = A₀exp (-k*t)

Where k is the radioactive decay constant and related to half-life as:

t (half) = ln (2) / k

Substituting k from the second equation, and putting the values:

14.2 = 15.3 * exp (-ln (2) * t / 5,730)

t = 617 years

The artifact is 617 years old, which means it is from 1371.