An ancient building was known to have been built 3,000 years ago. Approximately what proportion of Carbon-14 atoms are yet in the building's wooden framing compared to the number which were present at the time of its construction? (half life of 14C = 5,730 years)

83.2% of the original 14Carbon atoms present in the wooden framing of the ancient building at the time of its construction are still present today.

The half-life of Carbon-14 (14C) is 5,730 years, which means that after this time, half of the 14C atoms in a sample will have decayed. Using this information, we can estimate the proportion of remaining 14C atoms in the wooden framing of an ancient building that was constructed 3,000 years ago.

Since 3,000 years have passed, we can calculate the number of half-lives that have occurred by dividing the time elapsed (3,000 years) by the half-life of 14C (5,730 years). In this case, approximately 0.524 half-lives have occurred (3,000 / 5,730 ≈ 0.524).

With each half-life, the number of 14C atoms is halved. Therefore, after 0.524 half-lives, the proportion of remaining 14C atoms in the wooden framing can be estimated to be approximately [tex]0.5^{0.524}[/tex], which is about 0.832 or 83.2%. The rest have decayed over time. It is worth noting that this estimation assumes a constant rate of decay and no additional 14C uptake or loss since the construction of the building.

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