Radioactive decay: 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?

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To find the time it takes for a substance to decay to 4.0% of its original mass, we can use the half-life formula. Since 4.0% is the same as 4/100 or 1/25, this means the substance needs to go through enough half-lives to reduce to 1/25 of its original mass. Each half-life reduces the mass by half, so we need to find how many half-lives it takes to get to 1/25. 1/25 is 2^-x, where x is the number of half-lives. Solving 2^-x = 1/25 gives x ≈ 4.64 half-lives. Multiplying 4.64 by the half-life of 20,000 years gives approximately 93,000 years.

Radioactive Decay: the Material Used in Certain Nuclear Bombs Is