Question

You are on an archeological dig with a research team from the local university. The team unearths some pieces of an ancient wooden boat. When a sample of the wood is analyzed for carbon-14, scientists determine that 12.5% (or1/8) of the original amount of C-14 remains. If the half-life of C-14 is 5,730 years, how old is the wood from the boat?

Answer 1

Answer:

The wood from boat is 17190 years old

Explanation:

For first order radioactive decay-

                   $\frac{N}{N_{0}}=(\frac{1}{2})^{\frac{t}{t_{0.5}}}$

where N is remaining amount of radioactive elements after "t" time,$N_{0}$ is initial amount of radioactive element and $t_{0.5}$ is half-life of radioactive element

Here $\frac{N}{N_{0}}$ is 0.125, $t_{0.5}$ is 5730 years

Plug-in all the values in the above equation-

     $0.125=(\frac{1}{2})^{\frac{t}{5730}}$

    or,   t = 17190

so t is 17190 years or wood from boat is 17190 years old