Indefinitely since they are alpha emitters. This kind of radiation is stopped by almost anything like paper and the dead outer layer of skin and so is harmless unless you ingest the source.

Fact is, the waste that everyone is worried about (used nuclear rods) is not actually waste. 90%+ of the energy is still in there. It's just that the dominant reactor technology isn't designed to extract it. It would be dumb to bury this energy. It would be better to reprocess it like France does or even better, build the kinds of reactors that can directly use it as fuel.

Then you're left with fission products that you can bury it several kilometers underground in a deep borehole using oil/gas technology. It will naturally decay away in 300 to 600 years. Remember, most industrial toxins are toxic forever. There is no amount of time that will render it safe, and we don't even particularly try to isolate it because there's so much. It is only for nuclear waste that we try so hard. And it's only feasible because there's so little of it. All the spent nuclear rods (civilian) the US has EVER produced in 70 years fits in a football field at 30 feet high. Meanwhile a single coal plant produces 1100 tons of just ash a DAY. Not to mention all the air pollution and greenhouse gases. A single plant.

The waste aspect of nuclear energy is amazingly convenient in comparison.

Nah. You ignore the fact that alpha emitters (like literally anything else) can crap up their surroundings with micro-particles, and while you might be perfectly happy to hold an alpha emitting isotope in your hand you're gonna feel a lot different once you start ingesting them. As stated above your 600 year timescale is off by close to three orders of magnitude, and you appear to be pretending groundwater either doesn't exist or can't move. End of the day you're dead-ass wrong, as is evidenced by the fact that longterm stable storage of high level nuclear waste remains an unsolved problem despite the technology you're proposing having existed in some capacity for roughly a century before the first functional nuclear power plant went online.

> You ignore the fact that alpha emitters (like literally anything else) can crap up their surroundings with micro-particles

What on earth are you talking about? You realize you are full of alpha emitters?

> As stated above your 600 year timescale is off by close to three orders of magnitude

Nope, see this chart: https://whatisnuclear.com/img/ingestion-radiotoxicity-nuclea...

> you appear to be pretending groundwater either doesn't exist or can't move

That's why you bury it in rock where it doesn't move and we know it doesn't. Like the Permian Basin or where the Oklo natural reactors occurred in Gabon.

Oh yes, did you know nature formed fission reactors billions of years before we did ever existed? This always pisses off the hippies when I tell them. And guess what? The fission products from this natural process moved mere centimeters over 2 billion years.

This is a solved problem. It's just that some people desperately want it not to be.