Hi Donlinar Janko; Re: "First of all the quote talks about Pu. And second, the sentence reads like meant to say "the older you get, the sooner you'll die". True, but ... er... above all funny.
Actually, it's a paragraph, not a sentence. Here's the explicit logic for why that paragraph (see #reply-19823068 ) showed that there was no significant change to the half-life of uranium (i.e. significant enough to give a shelf life limit to fission bombs based on uranium).
If there had been a significant change to the half-life of Uranium, then there would have been a significant change to the level of radioactivity. The paragraph made it clear that even in weapon form, uranium is still nowhere near as radioactive as Plutonium. Therefore, even in weapons form, the half life of uranium must still be much longer than Plutonium. The half life of Plutonium is about 24,000 years. Radiation from an isotropic source falls off in intensity at about 1/r^2 (i.e. the surface area dilution, air doesn't absorb much). Therefore the half life of uranium, as used in bombs, is about 24,000 years * (70m/6m)* (70m/6m) = 3.3 million years.
While 3.3 million years is less than the usual half life of uranium, it's long enough that the loss of radioactivity will be negligible, at least for weapons stored for reasonable periods, which is what Maurice was talking about.
One could argue that the plutonium likewise had its half life also decreased by being weaponized. But for plutonium to be made to decay proportionately faster than uranium, and for uranium weapons to decay out in a few decades, the plutonium weapons would have "intense" thermal issues.
But why don't we cut to the chase and run the actual computation?
A fission bomb works by rapidly changing a subcritical mass of fissile material into a supercritical assembly, causing a chain reaction which rapidly releases large amounts of energy. In practice the mass is not made slightly critical, but goes from slightly subcritical (k=.9) to highly supercritical (k= 2 or 3), so that each neutron creates several new neutrons and the chain reaction advances more quickly.
en.wikipedia.org
Using a "neutron multiplication" factor of k = 0.9, it's easy enough to compute that each natural decay produces 0.9/(1 - 0.9) = 9 induced decays, for a total of 10 decays.
So there you have it, the decay rate of uranium in a weapon is increased by a factor of about 10. The half lives of uranium 235 is around 700 million years. I'm going to guess that there is no branching ratio involved, so the whole rate applies, so the half life in a weapon is about 70 million years.
It should be pretty clear that there isn't an engineering reason for choosing a k factor much closer to 1 than 0.9, as it will change the final (boom) k factor by a relatively small amount.
-- Carl
P.S. I was too busy to type this up last time. I'm glad that you asked. |
