Well, before you begin, perhaps we should explore precisely what we're talking about when we talk about nuclear fuel, when it's put in the reactor, when the reactor is running, and when it's taken out.
Nuclear fuel rods for a civilian reactor are enriched to about 5% U-235; the remainder of 95% is U-238, not U-234 (except in vanishingly small amounts). Natural uranium is about 99.3% U-238, 0.7% U-235, and an even smaller amount of U-234 (the enrichment processes, both gaseous diffusion and centrifugal enrichment, favor light isotopes, so both U-234 and U-235 are enriched).
The U-235 (5%) does all the fissioning (except for the very occasional U-234 or U-238 fission; this has a very much longer half-life than radioactive decay of either, however, so only a truly astronomically small fraction of the U-234 and U-238 undergoes fission). As the fuel is used, the U-235 undergoes fission; this results in likely radioactive fission products. The U-238 can absorb neutrons and the newly-formed U-239 will quickly decay to neptunium-239, and then to plutonium-239.
Since plutonium-239 is fissile, like U-235, some of it will undergo fission in the storm of neutrons inside the reactor, forming more fission products; however, this is not a majority process. The majority process is the fission of U-235. That's because the neutrons that are best at being absorbed by U-238 to form Pu-239 aren't the same energy as the neutrons that are best at being absorbed by U-235 and causing it to fission. The structure of the reactor is designed to maximize power, and therefore to moderate the neutrons so that they are the kind that cause the most U-235 fissioning, not the kind that convert U-238 to Pu-239; it's possible to make a reactor that makes neutrons that are the right energy to make Pu-239, of course, and this is called a "breeder" because it makes Pu-239. And, of course, the reason you do is because those neutrons are also not the right energy to cause Pu-239 fission; sure, it happens, but again, that's not the majority process, and that's controlled by the moderation.
So what we've got when we start is mostly U-238, with one atom in 20 being U-235, and one in a few thousand being U-234. As it's bombarded with neutrons, the U-235 fissions a lot, the U-238 is occasionally converted to Pu-239, the Pu-239 fissions sometimes, the U-234 is very occasionally converted to U-235, and occasionally a fission product (which was likely already radioactive) is converted to another isotope by the neutrons. As time goes on, the amount of U-235 decreases. As it does so, the amount of fission going on drops; this means that the moderation must be adjusted to keep the reaction going on. There's another problem, too; these products are also very often neutron absorbers and as their concentration increases, they damp the reaction by eating neutrons. Eventually, no amount of moderation decrease can keep the reaction going; there are too few neutrons being made, and too many things absorbing them. By this time, the amount of U-235 has decreased to perhaps 1-2% (Hindmost could probably come up with that figure; I'm too lazy to hunt further for a reference, but it's not all that important). A few percent of the U-238 has converted to Pu-239, and some of the Pu-239 has fissioned. This has taken a decade or more.
What you've got is still well over 90% U-238. Of the remainder, a couple percent is U-235, and a couple percent is Pu-239. The remaining six or eight percent is fission products, of varying levels of activity; a couple percent of this is high activity nuclear waste. But the higher level activity it has, the faster it decays. The bulk of the material is U-238, which has a half-life of 4.5 billion years; in terms of radiation hazard, not much because it has such a long half-life. There are high-activity isotopes in it, but storage for a few decades reduces this to the point where it is very little more active than the U-238 already is anyway. That's because the concentration of highly active isotopes was already in the single digits, and they decay very quickly; that's what "high activity" means.
Now, I won't misrepresent this; it's still radioactive after it's done its decades cooling off. But handling it for a limited period would be unlikely to harm the average person. You wouldn't want to handle it with your bare hands for a period of weeks on end, but more because you'd be likely to ingest some than because of anything it might do to your hands. You wouldn't want to eat it much of it; uranium is a low energy alpha emitter, so your skin (as has already been pointed out) is sufficient to stop the radiation, but if you were to ingest it, it could be a problem later on; however, it's important to point out here that the hazard would be far more a chemical poisoning risk than anything to do with radiation. In amounts small enough not to cause heavy metal poisoning and kidney failure, it would not pose much of a radiation hazard. No increase in human cancer has ever been reported in the scientific and medical literature as a result of exposure to natural uranium, and after the high-level isotopes have decayed, the spent fuel rods are not a great deal different.
Now, those are the facts. Let's see how many of them you already knew.
Well, gee, I'm sure glad you validated that from your infinite wisdom. I have a question: where is all this U-234 coming from? It's only five thousandths of a percent in the first place, even after enrichment, and U-234 doesn't get made by likely interactions inside a reactor.
So? It still only decays at a rate so low that only one half of it has done so in the lifetime of the Earth. And I repeat, why do you keep talking about U-234?
But it STILL only happens to half the atoms in a sample in four and a half billion years. I repeat, so? The incidence of it is still low. Furthermore, you're still talking about U-234. Which you have not demonstrated is relevant to the conversation since it only represents five one-thousandths of a percent of enriched uranium, and five ten-thousandths of a percent of natural uranium. Where is all this U-234 coming from?
Why does it have to be held in a vault for hundreds of thousands of years? In a hundred years, it's no more radioactive than natural uranium. And in thirty, it's only barely so.
And ignoring the facts is hysteria.
Let's talk about reality. The problem here isn't with civilian waste. The problem is with military waste. Military reactors use highly enriched uranium, and can "burn" a great deal more U-235 because they have a great deal more in the first place. This results in a very high concentration of fission products, and those products are very "hot;" furthermore, they remain so for a much longer time. Thousands or tens of thousands of years is not an unreasonable time to discuss spent military fuel remaining very dangerous in radiological terms. But if civilian use becomes widespread, the waste that it makes remains much lower level, and is therefore much less of a disposal problem than military waste. So basically, what opponents of civilian nuclear power are doing is equating military waste with civilian waste and claiming they're the same thing; add a dose of hysteria over teh invisuble nucular cancer rays, and there you have it.
And why do military reactors use HEU? That would be because most military reactors are on ships and submarines and they have to carry the fuel; that means that the more enriched the fuel, the less weight they have to carry per unit power, and the faster they can go. Simple, easy, obvious.
All of this is information you could easily have found out for yourself; much of it is already available in Wikipedia. Try "nuclear fuel cycle" and "uranium" for highly relevant articles.
Speaking of straw men...
So again, what we have here is hysteria driven emotional rhetoric. You don't know the difference between U-234, U-235, and U-238; you don't know that military and civilian fuel are different; you don't know the relation between specific activity and half-life; you don't know the difference between a breeder and a power reactor; you don't know the civilian "use once" cycle; you don't know what an integral fast reactor is; you don't know that there is thousands of times more uranium in seawater than in all the deposits of natural uranium we have ever discovered; you don't know that natural uranium is insufficiently radioactive to cause a single known case of cancer documented in the scientific or medical literature; and you don't know enough math to understand why if one in four and a half billion uranium atoms decays in a year, it means that one atom in 142,009,200,000,000,000 decays every second.
Overall, I'd have to say you know little of physics, and less of nuclear engineering. Which means that your opinions are based, not on facts, but on emotion. Which is basically what I said before. I'm pretty certain that there's no point in moving on to economics until you demonstrate a much firmer grasp of physics. So I think I'll stop here and wait to see if you have learned anything before I waste any more time.
