Question

Scientists found a fern fossil in some rock layers of the Grand Canyon. They estimated that a sample of one of the fossils originally contained 1000 carbon-14 atoms when it became 'fossilized', and at the time it was tested, it only contained 250 carbon-14 atoms. Look at the chart below. How old is the fossil?

Answer 1

This question is dealing with the half-life of carbon-14 which can be used to determine the age of a substance according to the following equation:

t = [ln(N/No)/(-ln2)] · t1/2

N = # of carbon-14 atoms presently = 250 atoms
No = # of carbon-14 atoms initially = 1000 atoms
t1/2 = half-life = 5730 years for carbon-14

We can now input all of the information into the formula to find the age of the fossil:

t = [ln (250/1000)/-ln2] x 5730 years

t = 11460 years

The fossil should be found to be roughly 11,460 years old.