The half-life of radioactive carbon-14 is 5730 years.If the 14C level in a sample of organic matter has been reduced to 0.200% of its original value, approximately how much time has passed? Radioactive decay follows first-order kinetics.

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Quizplus · Accepted Answer

The half-life formula for radioactive decay is $ t = \frac{\ln(\frac{N_0}{N})}{k} $, where $ t $ is the time, $ N_0 $ is the initial quantity, $ N $ is the final quantity, and $ k $ is the decay constant. Given that the half-life of carbon-14 is 5730 years and the level has been reduced to 0.200% (or 0.002 of its original value), we can calculate the number of half-lives that have passed as $ n = \frac{\ln(0.002)}{\ln(0.5)} \approx 8.965 $. Multiplying the number of half-lives by the half-life duration gives $ t \approx 8.965 \times 5730 \approx 51,400 $ years.

The Half-Life of Radioactive Carbon-14 Is 5730 Years