Final answer:
The age of the artifact can be calculated using carbon-14 dating, by comparing the current disintegration rate to a known rate in living samples. With a half-life of 5,730 years for carbon-14, the artifact is approximately 306 years old.
Step-by-step explanation:
To calculate the age of the artifact using carbon-14 dating, we first need to understand that the half-life of carbon-14 is about 5,730 years. This means that every 5,730 years, the amount of carbon-14 is reduced to half of its original amount due to radioactive decay. Using the provided activity rate measurements, we can then determine how many half-lives have passed since the artifact was from a living organism.
Given that a sample of fresh wood has an activity of 20 Bq and the artifact has an activity of 19 Bq, we can assume that not much time has passed, as the activity has not reduced significantly. To find the age, we'll use the formula:
N(t) = N_0 * (1/2)^(t/T)
where N(t) is the remaining amount of carbon-14, N_0 is the initial amount of carbon-14, t is the time that has passed, and T is the half-life of carbon-14.
In this case, using N(t)/N_0 = 19/20 and T = 5,730 years, we can solve for t:
(19/20) = (1/2)^(t/5730)
t = -5730 * log2(19/20)
t ≈ 306 years
Therefore, the age of the artifact is approximately 306 years.