Answer to Question #114048 in Atomic and Nuclear Physics for douglas

Question #114048
A wooden boat is found buried beneath the ocean floor. Scientists believe that timbers making up the boat had 16 g of carbon-14 in them when alive. They now have 4.1 g of carbon-14. How old is the boat if the half-life of carbon-14 is 5715 years?
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Expert's answer
2020-05-05T18:40:34-0400

Determine the decimal amount remaining: 4.116=0.25625\frac{4.1}{16}=0.25625.

Determine the number of half-lives: (0.5)n=0.25625(0.5)^n=0.25625,

nln0.5=ln0.25625,  n=ln0.25625ln0.5=1.964376n \ln 0.5=\ln 0.25625,\,\,n=\frac{\ln 0.25625}{\ln 0.5}=1.964376.

Determine years elapsed: 5715n=11226.45715 \cdot n=11226.4 years.


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