## anonymous one year ago Plutonium, the fuel for atomic weapons, has a half-life of about 24,400 years. An atomic weapon is usually designed with a 1% mass margin, meaning it will remain functional as long as the original fuel has decayed by no more than 1%, leaving 99% of the original amount. Estimate how long a bomb would remain functional. I used the equation y = Ca^t, with t = 24,400 and C is the original amount. I get the decay factor, a = 0.99997 and t = 335 years. But, someone told me the actual answer is 6 years. That doesn't make sense to me because, 0.99997^335 = 0.99 But 0.9997^6 = 0.99982

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1. anonymous

????? lol Questions about atomic weaponry idk if it would be legal for someone to anwser this lmao

2. whpalmer4

@Musicdude If you prefer, here's the question restated in unquestionably legal form. An element has a half life of 24,400 years. How long will it take for radioactive decay to reduce a sample of the element to 99% purity?

3. whpalmer4

@KuhlDad your information is incorrect about the bomb being disabled after only 6 years. Your calculation of the decay is pretty close: my answer is 353.79 years. $\frac{N(t)}{N_0} = \frac{1}{2}^{t/t_{1/2}}$$0.99 = \frac{1}{2}^{t/24400}$$0.99 = 2^{-t/24400}$ Take log of both sides and solve for $$t$$: $t\approx353.79 \ (\text{years})$ The primary short-term issue with short-term storage of modern nuclear weapons is the radioactive decay of the tritium boost gas, which has a half life of only about 12.32 years, which means about 5.5% of the tritium decays to helium by beta emission every year. As a result of this, nuclear weapons are on a regular maintenance schedule to have the tritium reservoirs replaced before the decay is an issue. After 6 years, the tritium quantity is down to about 70% of the original quantity, and given that tritium is hard to come by, that's probably a reasonable point at which to replenish rather than building larger reservoirs. Tritium costs about \$30,000 per gram these days. Plutonium pits (the core of a nuclear weapon) have a rather longer life-time. Current understanding is that plutonium pits in the US stockpile have an effective lifetime of a century or more. Loss of fissile material due to radioactive decay is not the only concern, but it is a driving factor for some of the aging considerations. All of this information is publicly available.

4. whpalmer4

The tritium gas is used as a booster and as a means of setting adjustable explosive yield in bombs that support doing so. I do not believe it is required to cause the primary fission explosion, but without it the bomb may not deliver the desired yield. That may be considered not functional by some, but you still wouldn't want to be anywhere close by!