The half-life of plutonium-239 is 24 100 years .Calculate the percent of a plutonium sample left after 100 years.

Question

Quizplus · Accepted Answer

The percent of plutonium-239 left after 100 years can be calculated using the formula for exponential decay, which is $N = N_0 \times (1/2)^{\frac{t}{T}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Given that the half-life $T$ is 24,100 years and the time elapsed $t$ is 100 years, the fraction of the initial amount left is $(1/2)^{\frac{100}{24100}}$. This fraction is approximately 0.997, or 99.7% when converted to a percentage. This calculation shows that only a very small fraction of the plutonium-239 would have decayed over such a relatively short period compared to its half-life.

The Half-Life of Plutonium-239 Is 24 100 Years