Question #174539

An ancient beam of wood is discovered during an archiological dig and carbon dated. They find that the sample contains 12.5% of the count rate of a similar mass of living wood. The half-life of the carbon isotope is 5600 years. Calculate the age of the ancient wood.


1
Expert's answer
2021-03-24T19:41:51-0400

Let’s use the formula for radioactive decay:


N=N0eλt,N=N_0e^{-\lambda t},NN0=eλt,\dfrac{N}{N_0}=e^{-\lambda t},ln(NN0)=ln(eλt),ln(\dfrac{N}{N_0})=ln(e^{-\lambda t}),ln(NN0)=0.693T1/2t,ln(\dfrac{N}{N_0})=-\dfrac{0.693}{T_{1/2}}t,t=ln(NN0)(0.693)T1/2,t=\dfrac{ln(\dfrac{N}{N_0})}{(-0.693)}T_{1/2},t=ln(12.5%100%)(0.693)5600 y=16803 y.t=\dfrac{ln(\dfrac{12.5\%}{100\%})}{(-0.693)}\cdot5600\ y=16803\ y.

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