A wooden object from a prehistoric site has a carbon-14 activity of 10 counts per minute (cpm) compared to 40 cpm for new wood. If carbon-14 has a half-life of 5730 years, what is the age of the wood?

Question

Quizplus · Accepted Answer

We can use the formula for exponential decay to solve for the age of the wood:
A = A0 * (1/2)^(t/T)
where A is the current activity (10 cpm), A0 is the initial activity (40 cpm), t is the time elapsed, and T is the half-life of carbon-14 (5730 years).
We can rearrange the formula to solve for t:
t = (ln A/A0) * T / ln 1/2
Plugging in the values given:
t = (ln 10/40) * 5730 years / ln 1/2
t = 11,460 years
Therefore, the age of the wood is approximately 11,500 years. Hence, the best choice is C.

A Wooden Object from a Prehistoric Site Has a Carbon-14