A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with
The activity of living organic matter, which is 0.230 Bq/g, the scientist determines how old the wood
Sample is, or more precisely, when the tree that the sample came from died. Carbon-14 has a
Half-life of 5730 years. If the activity of living matter has been constant over time, how old is the
Sample of wood?

Question

Quizplus · Accepted Answer

The age of the wood sample can be calculated using the formula for radioactive decay, which relates the initial activity (A0), the current activity (A), the decay constant (λ), and the time elapsed (t). The decay constant can be derived from the half-life (T1/2) of carbon-14 using the formula λ = ln(2)/T1/2. Given the half-life of 5730 years and the activities of the living matter (0.230 Bq/g) and the wood sample (0.144 Bq/g), the age of the sample can be calculated. The correct calculation leads to an age of approximately 3870 years, indicating that the tree died around 3870 years ago.

A Sample of Wood Has Been Recovered by an Archaeologist