What happened to the radiation that was supposed to last thousands of years in Hiroshima (1945)?

If you were expecting Hiroshima to be uninhabitable for thousands of years, you are (understandably, given the deplorable state of science education) making a whole bunch of errors in your understanding of radiation.
First of all, radiation isn’t magic death cooties. You and I are radioactive (traces of unstable potassium in our bones). My kitchen is radioactive (traces of unstable uranium in my granite countertop). If you have smoke detectors in your home (and you should) there’s a good chance they are radioactive (americium—quite, quite radioactive, but harmless unless you eat it or inhale it).
When it comes to radiation, the type, intensity, and duration of exposure mean everything.
The Little Boy bomb contained 64 kg (141 lbs) of highly-enriched uranium. What that means is that the government sorted through many, many, many trainloads of naturally occurring uranium ore to separate out the isotope needed for bomb-making. In nature (on Earth) uranium is mostly U238, which has a half life of 4.5 billion years. This extremely long half life means the energy it releases as radiation is spread out over far longer than the age of the universe, and is therefore harmless to life (it would be nearly harmless anyway, because it emits alpha particles that can be stopped by as little as the dead outer layer of your skin). U238 is too stable for use in making bombs. For bombs, you need uranium with much more U235, an isotope with a half life of a mere 700 million years. This means (roughly) that U235 is about 6.5 times more radioactive than U238, making it so intensely radioactive that…
… you can hold it in your hands with no ill effects at all (the gloves are to keep the metal clean and prevent any dust from making its way into the technician’s lungs or mouth—which would be dangerous).
Uranium is a naturally occurring ore that is more dangerous as a chemical toxin than for its weak radiation. When enriched to 80%, U-235 is weapons grade stuff—far more radioactive—but still not harmful unless ingested.
So, okay. What makes the stuff so dangerous? Well, when you put too much U235 in close proximity and under the right circumstances, you can create a chain reaction in which neutron release astronomically speeds up the decay of the atoms, making it astronomically more radioactive, making all that atomic energy come out astronomically faster. This can give you a lethal dose in a few seconds, or boil water to run a turbine, or go boom—all depending on how tightly and how quickly the atoms all come together.
The Little Boy bomb was little more than a lab experiment stuck in a cowling and hung under an airplane. Only about 1.5% of the uranium fissioned. The remaining 64 kg (141 lbs) went up in the mushroom cloud and spread across the Pacific ocean. Oh no! What have we done to mother Earth???
Not a lot, actually. The ocean already contains uranium. This is Earth, after all, and it’s a rocky planet, and the ocean contains the runoff from the mountains and the soup from hydrothermal vents. Every 20 cubic kilometers of unadulterated seawater already contains the same amount of uranium spilled by the bomb. The ocean contains roughly 1.332 billion cubic kilometers of water, so it already contains 66,600,000 times the amount of uranium released by the bomb. Put another way, the bomb had zero impact on the amount of uranium in the environment. Zero. Zilch. Nada.
But what about the 1.5% that actually fissioned? That’s your nightmare poison, right? Well, yes. Much of it transmuted into a cocktail of highly radioactive scariness, however:
Not all isotopes are equal. After an atomic bomb goes off, the isotopes that hurt people most are those with short half lives, not long ones. Isotopes like Niobium-95, Cerium-141, Barium-140 and in particular, Iodine-131 are extremely dangerous because they have half lives of only days. They release all their radiation quickly, so it can do a lot of damage—especially Iodine-131 which can be taken up by the body and transported to the thyroid gland, and Strontium-89 which can be taken up by bones. These fission products are truly monstrous—but they don’t last long. In weeks, they are no longer a reason not to enter the area unprotected. In a year (or two), they are effectively gone. That leaves longer-lived isotopes like Strontium-90 and Cesium-137, both with half-lives of about 30 years. These pose a long term cancer risk, but by now, they are basically gone too. The only effect they impose on today’s world is mucking up highly-precise scientific measurements.
So what’s this thousands of years business? Hysteria and misinformation, that’s what.
I do not, by this answer, mean to downplay the horrors inflicted by the bomb or to imply that radiation isn’t dangerous. It can be, but it can also be extremely helpful. Consider that Japan, first victim of nuclear warfare, entered World War II mostly over control of oil supplies in its South Pacific region of influence. After the war, nuclear power fueled a robust, peaceful economy. Now, Fukushima has the Japanese spooked. They are thinking of retreating from nuclear power. And if they do, it will be a mistake.
Even after Fukushima, the total number of members of the Japanese public killed by the peaceful application of nuclear energy remains 0. Meanwhile, several hundreds seem to have died due to panic over Fukashima, and 20,000 Americans die each year due to lung cancer caused by radioactive radon, most of which is dug up and spewed out the smoke stacks of coal-fired power plants. If Japan abandons nuclear power instead of upgrading to the newer safer designs now available, they will have to get their power at least partly from coal or natural gas. If they do that, for the first time since the bomb, radiation will start killing large numbers of Japanese*.
The point is, we don’t need to blindly fear nuclear energy. We need to respect it, understand it, and hold those who wield it to a high standard of public scrutiny. Ignorance is what we need to fear.

*In fairness, it probably already is. A significant number of lung cancers are caused by radioactive polonium contained in cigarettes. Polonium is another naturally occuring breakdown product of uranium (alongside radon) and for some reason, tobacco plants soak the stuff up, making it far more dangerous than it is in the environment at large.

Edit in response to several people who have contacted me, thanking me for saying, essentially, that “radiation is no big deal.” I did not say that. That is not true. What I said was, radiation can mean many different things, not all radiation is an immediate mortal threat, and (like anything useful in life) the benefits must be weighed against the costs.
Here are a few things I hope you will take away:
  1. The world is naturally full of radiation, and most of it is harmless or no more harmful than fire.
  2. Radioactive materials are not dangerous because they have half lives of thousands or millions of years. Indeed, the longer the half life, the less dangerous they are.
  3. Naturally occurring uranium and thorium are essentially harmless—radiologically speaking. But like lead, cadmium, and a zillion other elements and chemicals that fill our world, I wouldn’t want them tracked in my house.
  4. Even reactor or bomb grade highly enriched uranium and plutonium isn’t dangerously radioactive until used in a bomb.
  5. The Hiroshima and Nagasaki bombs (which is what the question was about) had a moderate radiological impact because they were small, they were air bursts, and they were terribly inefficient. Their fallout was pretty trivial in the grand scheme of nature.
  6. That doesn’t mean we should return to unfettered above ground nuclear testing. That was dumb and it’s good we stopped.
  7. That also doesn’t mean a global nuclear war would be “no big deal.” It would be. A very very big deal, not the least because it might be fought with weapons orders of magnitude larger and more efficient.
  8. Because the amount of radioactive material available for contact with living things is just as important as its half life. A nuclear war would not sterilize the planet or create the zombie apocalypse. It might raise global cancer rates for a generation. It might leave hundreds of ground zero areas dangerous for all but short visits for decades. It might cause the global economy and biosphere to collapse due to fear and fire respectively. We should avoid that.
  9. High level nuclear waste can indeed remain “dangerous” for thousands of years. That’s why we encapsulate it in multiple layers of protection. It’s only intensely radioactive for weeks or months after use, and the older it is, the less radioactive. Those fighting national waste storage under the presumption that such facilities would have to be perfectly sealed for millions of years are wrong—and are doing us all a disservice. In fact, the waste stored in those facilities will need to be monitored for centuries, but will not be so radioactive that a small release here or there would spell doom—even for those living nearby.
  10. Radiation decreases over time. Lots of other things don’t. There is a region in Appalachia that will remain sterile at least for thousands of years due to heavy metal contamination from open-pit smelting. Water supplies all across America are at risk from lead and cadmium leaching from thoughtless battery disposal. The PVC pipes we use to carry drinking water are a polymer of vinyl chloride—one of the most biotoxic substances known to man. There are several towns and regions that have had to be abandoned due to coal mine fires that cannot be extinguished. Global freaking warming. All these threats are manageable as long as the politicians take the lesson from Flint Michigan and listen to the scientists!
  11. Even with the accidents and poor waste handling so far, nuclear energy has done far, far more for humanity than it’s cost us. We need it, and we should be expanding its development alongside renewable energy sources, but we can and must hold the industry to much higher standards than we have in the past.
  12. The way to do that is not by fighting what we fear in ignorance, but in understanding it so we can intelligently regulate it as a society.

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