Carbon-14 (14 6c) dating is a method for finding the age of an organic artifact from the quantity of 14 6c it contains. carbon-14, an unstable isotope of carbon, follows a well-known sequence of decay processes. the decay constants of these processes have been well established, allowing researchers to determine the age of an artifact knowing both the original amount of 14 6c and the current amount.

in the lab, it is relatively easy to measure the activity of a sample and to estimate the mass of carbon in the sample. from these measurements, it is possible to find the age of the sample.

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 ratioof the mass of 14 6c to the total mass of carbon in the atmosphere is r, and the decay constant of 14 6cis ? . 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.

express your answer in terms of the mass ma of a 14 6c atom, mc, a, r, and ? .