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

Question

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.

Answer 1

Let’s use the formula for radioactive decay:

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