Answer to Question #113807 in Atomic and Nuclear Physics for Nya

Question

A wooden boat is found buried beneath the ocean floor. Scientists believe that timbers making up the boat had 8 g of carbon-14 in them when alive. They now have 2.3 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: $2.3/8=0.2875$.

Determine the number of half-lives: $(0.5)^n=0.2875$,

$n \ln 0.5=\ln 0.2875,\,\,n=\frac{\ln 0.2875}{\ln 0.5}=1.7984$.

Determine years elapsed: $5715 \cdot n=10277.66$ years.