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

Question

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?

Answer 1

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

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

$n \ln 0.5=\ln 0.25625,\,\,n=\frac{\ln 0.25625}{\ln 0.5}=1.964376$.

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