Wood deposits recovered from an archeological site contain 24% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.
A) The tree died 11,893 year(s) ago.
B) The tree died 13,425 year(s) ago.
C) The tree died 8,437 year(s) ago.
D) The tree died 10,770 year(s) ago.

Question

Quizplus · Accepted Answer

The age of the wood can be calculated using the formula for radioactive decay: $t = \frac{\ln(\frac{N}{N_0})}{k}$, where $N_0$ is the original amount of carbon-14, $N$ is the remaining amount, $k$ is the decay constant, and $t$ is the time in years. Given that $N/N_0 = 0.24$ and $k = 0.00012$, substituting these values into the formula gives $t = \frac{\ln(0.24)}{-0.00012} \approx 11,893$ years.

Wood Deposits Recovered from an Archeological Site Contain 24% of the Carbon