A sample containing carbon-14 contains 5.30 × 10⁻⁶ g of carbon-14 in it. If the age of the sample is 15,800 y, how much carbon-14 did it have originally? The half-life of carbon-14 is 5,730 y.

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Quizplus · Accepted Answer

The original amount of carbon-14 can be calculated using the formula for exponential decay, considering the half-life of carbon-14 is 5,730 years. Given the current amount is 5.30 × 10^-6 g and the age of the sample is 15,800 years, we can calculate the number of half-lives that have passed (15,800 / 5,730 ≈ 2.76). Using the formula $N = N_0 \times (1/2)^{t/T}$, where $N$ is the final amount, $N_0$ is the original amount, $t$ is the time, and $T$ is the half-life, we can solve for $N_0$. Rearranging the formula and substituting the given values, we find that the original amount of carbon-14 was significantly higher than the current amount, aligning with option B after calculating the exact value.

A Sample Containing Carbon-14 Contains 5