The material used in certain nuclear bombs is ²³⁹Pu,which has a half-life of about 20,000 years.How long must we wait for a buried stockpile of this substance to decay to 4.0% of its original ²³⁹Pu mass?

Question

Quizplus · Accepted Answer

To find the time it takes for a substance to decay to 4% of its original mass, we can use the half-life formula. Since 4% is the same as 4/100 or 1/25, we need to find how many half-lives it takes to reach this fraction. Doubling 1/2 repeatedly to find when it reaches 1/25 or less, we find it takes 5 half-lives (1/2^5 = 1/32, which is less than 1/25). Multiplying the half-life of 20,000 years by 5 gives us 100,000 years. However, due to a calculation oversight, the correct answer is actually closer to 93,000 years, considering the precise decay process and logarithmic calculations involved in determining the exact time for a substance to decay to a specific percentage of its original mass.

The Material Used in Certain Nuclear Bombs Is 239Pu,which Has

The Material Used in Certain Nuclear Bombs Is ²³⁹Pu,which Has