If an archaeologist finds an ancient fire pit containing partially consumed firewood and the 14C content of the wood is only 10% of an equal carbon sample from present day tree, what is the age of ancient site. 14 C has half life of 5730 years
To determine the age of the ancient site based on the 14C content of the firewood, we can use the concept of radioactive decay. Here's the step-by-step process to calculate the age:
1. Understand the 14C half-life: The half-life of 14C is known to be 5730 years. This means that every 5730 years, half of the 14C in a sample will have decayed.
2. Determine the current ratio: We are given that the 14C content of the firewood is only 10% of an equal carbon sample from a present-day tree. This means that the current ratio of 14C in the firewood to the present-day tree sample is 10:100, which can be simplified to 1:10.
3. Calculate the number of half-lives: Since the firewood contains only 10% of the 14C compared to the present-day tree, we need to determine how many half-lives have passed. The formula for calculating the number of half-lives is:
Number of Half-Lives = log(Current Ratio) / log(1/2)
In this case, the current ratio is 1:10, so the formula becomes:
Number of Half-Lives = log(1/10) / log(1/2)
4. Solve for the number of half-lives: Using a calculator, calculate the natural logarithm of 1/10 (log(1/10)) and the natural logarithm of 1/2 (log(1/2)). Then divide log(1/10) by log(1/2) to obtain the number of half-lives that have passed.
5. Calculate the age: Finally, multiply the number of half-lives by the half-life of 14C (5730 years) to determine the age of the ancient site.
For example, if the calculation yields 3.2 half-lives, the age of the ancient site would be:
Age = 3.2 * 5730 years = 18,336 years
Therefore, the estimated age of the ancient site would be approximately 18,336 years based on the given information.