Posted: March 13th, 2017

Assume that, at any time, 14 6C is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14 6C.

Find the age t of a sample, if the total mass of carbon in the sample is mc, the activity of the sample is A, the current ratio of the mass of 14 6C to the total mass of carbon in the atmosphere is r, and the decay constant of 14 6C is λ. Assume that, at any time, 14 6C is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14 6C. Also assume that the ratio of mass of 14 6C to total carbon mass in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14 6C atoms in the sample was set.