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A sample of wood from an archaeological excavation is dated by using a mass spectrometer to measure the fraction of 14C atoms. Suppose that 173 atoms of 14C are found for every 2,561,140,426,409,936 atoms of 12C in the sample. What is the wood’s age? The half-life of carbon 14 is 5730 years.The natural abundance of carbon 14 in a sample of carbon is 1.3 x 10-12 per 1 of carbon 12.

Answer :

[tex]\begin{gathered} \frac{N}{N_o}=(\frac{1}{2})^{\frac{t}{T_{1/2}}} \\ where: \\ N=173 \\ N_0=\frac{173}{2561140426409936}\cdot2561140426409936 \\ N_o\approx1729.8 \\ T_{1/2}=5730 \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} \frac{173}{1729.82}=(\frac{1}{2})^{\frac{t}{5730}} \\ log(0.1)=\frac{t}{5730}log(0.5) \\ t=5730(\frac{log(0.1)}{log(0.5)}) \\ t\approx19033.788 \end{gathered}[/tex]

Answer:

Approximately 19034 years

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