Question

The material used in nuclear bombs is Pu 239 with a half-life of about 20,000 years. How long must we wait for a buried stockpile of this substance to decay to 4% of its original Pu 239 mass?

I got t = 92896.85 years
approx= 93,000 years

Answer 1

The half-life equation:
\[y=Ce^{rt}\]
You're given that the half-life is 20,000, which means that at \(t=20,000\), \(C\) will have decayed to half its original value.
\[\frac{1}{2}C=Ce^{20,000r}\]
or
\[\frac{1}{2}=e^{20,000r}\]
Solve for \(r\):
\[\frac{\ln(1/2)}{20,000}=r\]
To find the time it takes for 4% to remain, we solve for \(t\):
\[0.04=e^{rt}\\
\frac{\ln0.04}{r}=t\approx 92,877\]
The discrepancy between our results is probably a consequence of rounding.

Answer 2

thank you.