Answer to Question #66751 in General Chemistry for Adrian

Question

The bones of a prehistoric bison were found to have a C-14 activity of 2. 80 dis/min gram of carbon. Approximately, how long ago did the animal live? Given that the half life of Carbon-14 isotope is 5668 years.

Answer 1

The decay rate of carbon-14 in fresh material today is 13.6 counts per minute per gram.
1) Decimal fraction of C-14 remaining:
2.80 / 13.6 = 0.20588235
2) Amount of half-lives elapsed:
(1/2) n = 0.20588235
n log 0.5 = log 0.20588235
n = 2.42857146
3) Length of time elapsed:
5668 yr x 2.42857146 = 13765 years