Carbon-14 (¹⁴C)dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago.If this is true,then the amount of ¹⁴C absorbed by a tree that grew several centuries ago should be the same as the amount of ¹⁴C absorbed by a similar tree today.A piece of ancient charcoal contains only 24% as much of the radioactive carbon as a piece of modern charcoal.How long ago was the tree burned to make the ancient charcoal? (The half-life of ¹⁴C is 5715 years.)Round your answer to the nearest integer. A) 2,776 years B) 30,751 years C) 2,781 years D) 11,767 years E) 11,772 years

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Quizplus · Accepted Answer

The ancient charcoal has 24% of the radioactive carbon compared to modern charcoal, which means it has gone through multiple half-lives of Carbon-14 (5715 years). To find the number of half-lives, we use the formula for exponential decay: $N = N_0 \times (1/2)^{t/T}$, where $N$ is the remaining amount of substance, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life period. Solving for $t$ when $N/N_0 = 0.24$, we find that it corresponds to approximately two half-lives, leading to around 11,430 years. However, the exact calculation should be done using logarithms, which gives a value closer to the option provided, indicating the tree was burned approximately 11,767 years ago.

​Carbon-14 (14C)dating Assumes That the Carbon on the Earth Today

Carbon-14 (¹⁴C)dating Assumes That the Carbon on the Earth Today