Question

Measurements of radioactive C-14 isotope in a mammoth's bone showed that only 1/1,024th of the original isotope remains today. Since the half-life of C-14 is 5,730 years, the best estimate for the age of this bone is _________ years.

Answer 1

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues. When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14. The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay. In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years. The age of the fossil can be then determined usng the formula:

t = [ln(n/n0)]/(-0.693)]xhalf life

t=[ln(1/1024)/(-0.693)]x5730

t=57312 years