One material used in nuclear bombs is $239 \mathrm { Pu }$, with a half-life of 24,000 years. How long must we wait for a buried stockpile of this substance to decay to $1 / 1000$ of its original activity?

Question

Quizplus · Accepted Answer

To find the time it takes for a substance to decay to $1/1000$ of its original activity, we can use the formula relating the amount of substance remaining to the half-life of the substance: $N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time, and $T$ is the half-life. For $N/N_0 = 1/1000$, we can set up the equation $1/1000 = \left(\frac{1}{2}\right)^{\frac{t}{24000}}$. Solving for $t$, we find that $t = 24000 \log_2(1000) = 24000 \times 10 = 240,000$ years.

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One Material Used in Nuclear Bombs Is $239 \mathrm { Pu }$