Answer to Question #160172 in Atomic and Nuclear Physics for Ulrich

Question #160172
A wooden artifact is found in an ancient tomb. Its carbon-14 activity is measured to be 60% of that in a fresh sample of wood from the same region. Assuming the same amount of C-14 was initially present in the artifact as is now contained in the fresh sample, determine the age of the artifact.
1
Expert's answer
2021-02-18T18:56:31-0500

Let’s use the formula for radioactive decay:


"R=R_0e^{-\\lambda t},""\\dfrac{R}{R_0}=e^{-\\lambda t},""ln(\\dfrac{R}{R_0})=ln(e^{-\\lambda t}),""ln(\\dfrac{R}{R_0})=-\\dfrac{0.693}{T_{1\/2}}t,""t=-\\dfrac{ln(\\dfrac{R}{R_0})}{0.693}T_{1\/2},""t=-\\dfrac{ln(0.60)}{0.693}\\cdot5370\\ yr=4224\\ yr=4.2\\cdot10^3\\ yr."

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