The radioactivity due to Carbon-14 measured in a piece of a wooden casket from an ancient burial site was found to produce 20.0 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160. counts per minute. The half-life of Carbon-14, a beta emitter, is 5730. years. Thus we would estimate the age of the artifact to be about
A) 14,800 years
B) 17,200 years
C) 11,500 years
D) 20,000 years
E) 5,700 years

Question

Quizplus · Accepted Answer

The age of the artifact can be estimated using the formula for radioactive decay, which relates the initial and final activities (or counts per minute in this case) to the half-life of the decaying substance. Given that the initial activity is 160 counts per minute and the final activity is 20 counts per minute, we can calculate the number of half-lives that have passed. The activity has decreased by a factor of 8 (since 160/20 = 8), which corresponds to 3 half-lives (since 2^3 = 8). Therefore, the age of the artifact is 3 half-lives of Carbon-14, which is 3 * 5730 years = 17,190 years, rounded to 17,200 years.

The Radioactivity Due to Carbon-14 Measured in a Piece of a Wooden