What amount of Plutonium-239 remains after 96,000 years, starting from 1 gram, given its half-life of 24,000 years?

To determine the amount of Plutonium-239 remaining after 96,000 years, we need to apply the concept of half-lives. The half-life of Plutonium-239 is 24,000 years, meaning that every 24,000 years, half of the original amount will have decayed.

First, we calculate how many half-lives are contained within 96,000 years:

96,000 years / 24,000 years per half-life = 4 half-lives.

Next, we start with the initial amount of 1 gram and see how it changes after each half-life:

• After the first half-life (24,000 years), the amount reduces to 0.5 grams.

• After the second half-life (48,000 years), it reduces to 0.25 grams.

• After the third half-life (72,000 years), it reduces to 0.125 grams.

• After the fourth half-life (96,000 years), it reduces to 0.0625 grams.

Thus, after 96,000 years, starting from 1 gram, the amount of Plutonium-239 remaining is 0.0625 grams. This consistent reduction reinforces the concept of exponential