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We don't know that it will be capable of being turned into fuels.
Wait long enough and they'll be able to turn it into breakfast cereal. A lot of this waste breaks down on it's own anyway, it just takes hundreds or thousands of years, but eventually it becomes totally harmless.I know most people hear the words "nuclear waste" and think of yellow barrels with glowing green goop leaking out of it that will instantly mutate anything that comes near, like something out of an episode of "Captain Planet" or something. That's the problem, people are getting all their information on this subject from hazy memories of 80's cartoons.
It eventually becomes harmless but over that time the risk of a catastrophic failure builds up. I mean even if there's a.69% chance of such a failure in any given year, after 1000 years the odds of a failure occurring is 1 in 2.
I don't think odds are meant to be viewed cumulatively like that. But it's actually a remarkably small amount of waste that is even that bad, if you collected all the nuclear waste in the world right now, it would all fit very comfortably with lots of room to spare inside of a modern sports stadium and only a tiny fraction of that is still dangerous after a few centuries. I mean, could there be a disaster? Not really, it would be a pretty easily contained disaster. The waste is the least dangerous byproduct of nuclear power. The live fuel rods are infinitely more dangerous and capable of creating a disaster.
When you're dealing with radioactive materials (probably the most toxic materials in existence) even a small amount of waste could do quite a bit of damage. If something like a large explosion happened at one of those storage cites it would be difficult to contain it. And the odds should be viewed cumulatively until the waste is no longer radioactive.
Actually I think the way you calculated those odds to compound is simply inaccurate. You went the wrong direction, lol.
Odds compound over time, that's how statistics work.
Not in the example you gave, the odds of a.69% failure rate over 1,000 years?Would be a series of one second intervals, each with a.69% chance of failure. The previous seconds would have no impact on any future seconds. I mean, if it didn't fail yesterday, it's not any more likely to fail tomorrow just because it didn't fail yesterday. This isn't "Final Destination." Also, it's not hard to contain this stuff safely in small amounts, it's EXPENSIVE, and you need the exact right materials, but it's not like we don't know how to do it.
The odds of it happening at least over the course of 1000 years is 50/50. The odds of an event happening n number of times in a row is the probability of it happening once (P) to the power of n (P^n). If we have a.069% chance of an event happening in a year, there is a 99.931% chance of it not happening. This means that it not happening over n number of years (.9931)^n. If we want to know how many years have to pass for there to be a 50% chance of no disaster occurring (which also means that there's a 50% of chance of a disaster occurring) we solve for n in this equation: .5 = .9931^n. Take the natural log of both sides and we get ln (.5) = n*ln (.99931). Divide ln (.5)/ln (.99931) and we get n = 1004 years.
And the space disposal option has an "error cost" that I don't think most people would consider acceptable.https://www.youtube.com/watch?v=WFZwI10HEsw
Wow! One failure and a huge nuke would detonate!
Not entirely, there wouldn't be enough energy density to trigger a nuclear chain reaction leading to the nuclear explosion BUT it will spray radioactive debris all over the place.