Why is Hiroshima habitable now when the half life of uranium-235 is 700 million years?

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Mudassir Ali 9 months 1 Answer 96 views

Answer ( 1 )

  1. Because the half life of U235 is 700 million years.

    Think about it. Assume that half* the uranium was split during the chain reaction, leaving the other half to just be extra uranium that settled into the ground. [Edit, in fact, it was more like 2 percent that fissioned, with 98% left over.]

    That gives you well short* of a megaton worth of energy, to be released over 700 million years and distributed over a region of at least 100 square kilometers. [Edit, the yield of the bomb itself was more like 10 or 20 kilotons, but since most of the U235 did not fission then and there, we have to multiply by 50 or so to get the energy that will eventually be released. So it’s not as “well short” of a megaton of latent energy left to consider as I had originally thought. It is, though, at worst in the vicinity of 1 megaton.]

    So how much energy is released per square meter per year? We gave ourselves 4E15 joules, which is one megaton. That was very generous. But we have to divide by 7E8 for starters, to get the yearly release. That takes us to about 6E6 joules per year. Now we divide by 100 to get 6E4 joules per square kilometer, and then by E6 to get 6E(-2) joules per square meter per year.

    Sunlight reaching the surface comes to a few hundred joules per second. So you’re getting ballpark a thousand times as much sunlight per second as you’re getting radioactive release of energy from uranium decay per year. Some nontrivial fraction of that sunlight is in the UV part of the spectrum. So to simplify, one second in the sun is more likely to give you cancer than one year living in the company of that extra radiation.

    [Edit: the question was about the danger specifically from Uranium. The less trivial danger, which is still by now negligible, arises from radioactive isotopes of strontium and cesium. The uranium that fissioned would have had a fair proportion of its fission products being of that type. These elements mimic calcium and sodium which the body uses. If garden plants incorporate them and you eat it, you get shot up from the inside by the radiation their decay emits. With half lives of 30 years or so, even these are by now much reduced in intensity, but if you’re intent on being very careful, don’t eat veggies from gardens planted at ground zero.]

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