The time radioactive waste must be stored depends on the type of waste and radioactivity.
The back-end of the nuclear fuel cycle, mostly spent fuel rods, contains fission products that emit beta and gamma radiation, and actinides that emit alpha particles, such as uranium-234 (half-life 245 thousand years), neptunium-237 (2.144 million years), plutonium-238 (87.7 years) and americium-241 (432 years), and even sometimes some neutron emitters such as californium (half-life of 898 years for californium-251). These isotopes are formed in nuclear reactors.
Sources: https://en.wikipedia.org/wiki/Radioactive_waste#cite_note-3
We purify the material, yes.
If the ore grade is lower (e.g., 0.05%), you’d need ~280–300 kg of ore per kg of U-235.
When a hypothetical water contamination would occur in a natural deposit with a 0.05% density, it would contaminate water less than if it would occur with a purified source.
“The dose makes the poison.” You may have heard the proverb.
The higher the dosage, the higher the potential health risk. Which is exactly why the purified material is so much more dangerous than the natural occuring sources.
You also assume controlled environments, deep in old salt mines. Have a look at this: https://en.wikipedia.org/wiki/Santa_Susana_Field_Laboratory#cite_note-VCR_2003-02-19-33
“Lopez described the cleanup of the heavily polluted sodium burn pit, a six-acre site where Rocketdyne disposed of massive amounts of radioactive waste. The modus operandi included chucking barrels of radioactive sodium into the sludgy pond and firing a gun at the canisters, which would then explode, releasing radioactive contaminants into the air.Lopez said that the pit has now been excavated ten to 12 feet down to the bedrock, resulting in the removal of 22,000 cubic yards of soil.”
They did so, because the barrels wouldn’t sink to the ground of the pond.
There isn’t even a guarantee, for correct disposal. One could pocket life changing money by chucking barrels into the sea, today.
But that was not my point, my point was we cannot assume a controlled environment, even to the best of our abilities and knowledge, in timespans we haven’t even been able to measure our own history in.
I am not totally against nuclear energy, it has the highest energy density possible. Heavier atoms aren’t stable enough. The periodic table ends with these elements for a reason.
But the potential dangers, stemming from them are unimaginable. Because they exceed our very own existence as a species.