Asample of wood from the remains of a ship was found to contain 40.0% of c-14 as of ordinary wood found now. if the half-life period of c 14 is 5770 years, find the number of years elapsed. (round your answer to the nearest whole number)

7628 y

Explanation:

Carbon-14 is radioactive and it follows the first-order kinetics for a radioactive decay. The first-order kinetics may be described by the following integrated rate law:

Here:

is the mass, moles, molarity or percentage of the material left at some time of interest t;

is the mass, moles, molarity or percentage of the material initially, we know that initially we expect to have 100 % of carbon-14 before it starts to decay;

is the rate constant;

is time.

The equation becomes:

Given:

Solve for time:

In this case: