An archaeologist finds the 14C in a sample of 2.10 g of material to be decaying at 107 Bq. A modern 1.00-g sample of the same material decays at 151 Bq,and assume this rate has also held in
The past. The half-life of 14C is 5730 years. How old is the sample?

Question

Quizplus · Accepted Answer

The decay rate is proportional to the amount of radioactive material present. The ratio of the decay rates of the two samples is equal to the ratio of their masses, so the mass of the ancient sample is 2.10 g / 1.00 g = 2.10. The decay rate of the ancient sample is 107 Bq / 2.10 = 51.0 Bq/g. The decay rate of a modern sample is 151 Bq / 1.00 g = 151 Bq/g. The ratio of the decay rates is 51.0 Bq/g / 151 Bq/g = 0.338. The half-life of 14C is 5730 years, so the age of the sample is 5730 years * log(2) / log(0.338) = 8980 years.

An Archaeologist Finds the 14C in a Sample of 2