Carbon-14 dating relies on comparing the activity of 14C in an archaeological sample with that in living matter. Assume the activity of 14C in living wood is 15.3 disintegrations per minute per gram of carbon.
For an ancient wooden artefact the measured activity is 3.83 ± 0.15 dpm g−1. The half-life of 14C is 5730 years.
(i) Derive an expression for the age t of the sample in terms of the measured activity A and the activity A0 of living wood.
(ii) Using the data above, calculate the most probable age of the artefact.
(iii) Estimate the uncertainty in the age arising from the stated measurement uncertainty in activity. State your final answer as t±Δt in years.