The story changes significantly if we start using breeder reactors and other designs.
Uranium is everywhere. While there are mines that have extremely high concentrations of Uranium, it is present in trace amounts in almost everything from granite to sand to soil to groundwater. There are 4 billion tons of Uranium dissolved in the oceans. A number of projects have looked at filtering and extracting it from the oceans. It's relatively expensive to extract it from seawater, but not insane--4x-10x the cost of mining. We won't run out.
https://deeply.thenewhumanitarian.org/oceans/articles/2018/0...
> I believe I read the estimate is something like 50 years?
It's more like 200 years. And that's "economically accessible", not accessible.
https://www.scientificamerican.com/article/how-long-will-glo...
> estimate is something like 50 years
those are pretty pessimistic estimates.
From a 2009 article on Scientific America
According to the NEA, identified uranium resources total 5.5 million metric tons, and an additional 10.5 million metric tons remain undiscovered—a roughly 230-year supply at today's consumption rate in total
the extraction of uranium from seawater would make available 4.5 billion metric tons of uranium—a 60,000-year supply at present rates
fuel-recycling fast-breeder reactors, which generate more fuel than they consume, would use less than 1 percent of the uranium needed for current LWRs. Breeder reactors could match today's nuclear output for 30,000 years using only the NEA-estimated supplies.
Since the fuel is cooled in water ponds for decades before it is processed, even in the case of a nuclear industry boom there's ample lead time to alter the plans if running out of materials seems to become an issue. I'd be much more worried about usage of oil as it is the base material for a lot of different things like medicines, and we're burning the stuff away (granted, we can do synthetic hydrocarbons, but the whole thing with oil is a bigger problem in my books than running out of uranium; it's still there to be retrieved if it really comes down to it).
If it's "undiscovered", presumably that 0.5 metric tons amounts to spurious precision. Call it ten million, and it becomes clear that it's a wild guesstimate.
Also: the location of these Uranium deposits is not evenly distributed. I understand that substantially all of France's Uranium, for example, comes from Niger, a politically-unstable country where much of the mining is controlled by the Wagner Group.
https://www.lemonde.fr/en/les-decodeurs/article/2023/08/04/h...
( Or, if you prefer, the Nuclear Energy "Red Book":
https://www.oecd-nea.org/jcms/pl_79960/uranium-2022-resource...
In France, although no domestic uranium exploration and mine development activities have been carried out since 1999, majority government-owned Orano (formerly Areva) and its subsidiaries remain active abroad.
As of 2020, Orano S.A. has been working outside France, focusing on discovery of exploitable resources in Canada, Gabon, Kazakhstan, Mongolia, Namibia and Niger. In Canada, Kazakhstan and Niger, Orano is also involved in uranium mining operations.
In addition, as a non-operator, Orano holds shares in several mining operations and research projects in different countries. In 2020, Orano started exploration in Uzbekistan.
Total nondomestic exploration expenditures remained relatively steady from 2017 to 2018 at about USD 30 million per year, before declining by 17% to around USD 25 million in 2019 and 2020.
)So: very short half-life is good, because the element turns into something else very quickly and ceases to be a problem. This is the nanoseconds-to-days range.
Very long half-life: not actually all that radioactive. e.g. U238 itself with a half-life in the billions of years.
Medium half-life: emits a dangerously high level of radiation in the process of decaying. This is the real problem stuff as "medium" can mean "centuries".
That is part of why this "no human should set foot for 100,000 years" is silly. We only have recorded history going back a few thousand years, and all of civilisation was invented in that time. If humans are exist in 100,000 years we'll be using that century-long half life material for something important.
The sun is also a third of a million times the mass of the entire planet, or about 1.4 billion times the mass of all our oceans.
And the power output being in the form of ionising radiation is really bad: the power density of the core of the sun is 276.5 W/m^3, but in a form which will, if you leant against it for a minute and given reasonable guesses as to your body mass and shape, give you a remaining conscious lifetime of vomiting, diarrhoea, seizures, bleeding everywhere inside and out, relieved only by being followed with a coma after about an hour then death within a day or two.
(That's ignoring the fact that it's also hot and dense and would immediately explode, it's just the effect of the radiation coming from it).
> If humans are exist in 100,000 years we'll be using that century-long half life material for something important.
There are three possible futures: business as usual, collapse, transcendence/singularity.
With business as usual, there's a fairly good chance that everything from our era will be forgotten and dismissed as myth and legend.
With collapse, all of society might of forgotten how the abstract concepts of "money" and "writing" work, reinvented them, gotten up to our level, and then collapsed again 50 times over.
With the singularity: the planet itself and every star visible to the naked eye (and many which aren't) may have been physically disassembled in that time frame.
I think we should be the kind of civilisation that plans for how to minimise the damage of bad outcomes, even if only to make sure we don't mess up the "singularity" option.
This is the basis of the radiothermal generator (RTG); but generally, the spent fuel is deemed spent in the first place because it's no longer emitting enough heat/neutrons to be worth keeping in the reactor. It's already got to the point of "it's no longer worth the hassle of handling this and dealing with all those neutrons/gamma radiation in exchange for a mediocre amount of warmth".
It's in a fission reactor and those isotopes aren't fissile, and aren't a huge proportion of the "spent fuel" to begin with. To be useful it has to be separated.
Short-lived highly radioactive substances are commercially valuable as radiation sources. Medium-lived radioactive substances are useful in RTGs (not fission reactors). Long-lived radioactive substances are often fissile and therefore useful as reactor fuel.
But none of them are useful when they're all mixed together, because what they're each useful for is a different thing. So separate them.
An atomic bomb is when you convince a lot of Uranium-235 or Plutonium to decay all at once in an uncontrolled way.
A nuclear reactor is what happens when you convince material to decay at a controllable rate.
It's way more complex than that but you can look up the rest, e.g. "Nuclear chain reaction".
Where I think you're going with this is
https://physics.stackexchange.com/questions/594598/destroyin...
tl;dr: it's more trouble than it's worth, since you need radioactive materials as the neutrons sources, and stray neutrons tend to bump into other matter and cause yet more radioactive waste.
So if you could control and direct these NPAP's to behave like a Newton Cradle, you could accelerate them away faster?
Something for CERN to try maybe?
I get the impression that your understanding of the current state of particle physics is approximately 80 years behind the state of the art. You're catching up with Leo Szilard's ideas in the 1930s
As far as the parent comment's implied question, "and is that useful for radioactive waste disposal?" the answer is a strong "no, there are far better uses for the energy required, within and outside of radioactive waste disposal", including using this energy instead of energy from the nuclear reactor that makes waste.
The key thing here is "known". In order to "know" of the economic viability of a mining source you need to invest serious money. Mining companies have serious money, and they invest them to "prove" new reserves, because that's how they can get loans from banks. But once the reserves exceed whatever demand there is in the world for more than a hundred years, there's absolutely no incentive to keep exploring further. That's where we are now: there are about 8 million tons of proven uranium reserves [1]. The annual production fluctuates very slightly around 50,000 tons [2]. At the current production levels we have more than 150 years of proven reserves.
But if we were to suddenly double the number of reactors, we would very quickly double the proven reserves. If we were to multiply 100-fold the number of reactors, we'd multiply the proven reserves by 100, or more likely more than that.
In the end there is absolutely no limit. The current market price of uranium is about $130 per kg. It is estimated that it can economically be extracted from seawater for $1000/kg, so less than a factor of 10. Such a cost would not increase the cost of electricity by even one cent per kWh ( see the math in the notes).
As for breeder reactors or other designs. The current generation reactors produce about 40 to 60 GWday of energy from 1 ton of uranium fuel (which is generally enriched to close to 5% U-235). New designs will increase this number (called burnup) to 100 [3] and some even to 180, but generally not because they are more efficient, just because they'll use fuel enriched to up to 20% U-235. There are 2 designs that will exceed that, but they are supposed to burn thorium rather than uranium. We have easily 100 times less experience with thorium than uranium, so I wouldn't hold my breath that it's a piece of cake to achieve higher burnup with it. In theory we could, but practice finds ways to disagree with theory.
Notes: the math of 1 cent per kWh: you need about 10 tons of natural uranium to produce one ton of fuel-grade uranium, and with that you get about 50 GWd, or 50 x 24 = 1200 GWh = 1.2 billion kWh of electricity. 10,000 kg at $1000/kg is $10 MM for 1.2 billion kWh, or 0.83 cents/kWh.
[1] https://en.wikipedia.org/wiki/List_of_countries_by_uranium_r...
[2] https://world-nuclear.org/information-library/facts-and-figu...
Where did you get that notion?