Answered

IDNLearn.com is your reliable source for expert answers and community insights. Our platform offers reliable and detailed answers, ensuring you have the information you need.

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.

Sagot :

[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

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.