Ace has the facts.
Containment has not failed. The part that blew off the reactor building is, essentially, a sheetmetal building atop the actual containment vessel for the reactor. It's there to house the machinery used for servicing the core, and it acts to contain stray radiation when the core is opened (such as when fuel elements are being replaced). The core itself, however, is not open to the environment at this time.
The core is, however, far too hot. The cooling system has failed; the core got so hot that it began producing hydrogen; venting that hydrogen is what caused the destruction of the sheetmetal shack atop the containment vessel.
What we're looking at right now is, in fact, another Three Mile Island, not another Chernobyl.
They say that the area around the damaged reactor is being exposed to radiation "eight times normal" but that only amounts to an exposure of about 800 millirem per year at sea level. (Normal is around 100.) The people living nearby don't even need to skip their next chest x-ray at that kind of exposure level.
If you had camped out atop the failed TMI reactor for the entirety of that event, you would have received a total dose of 1,500 millirem. If you go get an angiogram, you're exposed to more than ten times that amount of radiation, and over a much shorter period.
800 millirem is nothing.
The biggest problem is keeping the core from melting. It's even fine if it melts partially, the way the TMI core did, as long as it stays within the containment building; and the containment building is designed specifically to keep that stuff inside under all but the most dire of circumstances.
What caused the problem? A failure of the flow of coolant. What caused that?
The tsunami inundated the grounds of the plant and contaminated the fuel supply for the emergency backup generators that are supposed to power the cooling pumps in the event of an emergency exactly like this one. The generators ran for about an hour, then quit, and that's when the problems started.
The media, of course, are all reporting this as if someone set off an atomic bomb in downtown Tokyo.
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Rod Adams has it right.
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As for me, I got up after my five-hour nap and got a bacon mofo; now I'm gonna play WoW, at least for a little bit.