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nuclear waste is so incredibly dense

Yes and no. Most current fuels are Uranium or Plutonium. Both between 19 and 20 g/cm3. For reference, liquid water is approximately 1 g/cm3. Unspent fuel is a similar weight to gold.

“Spent” U238 is usually around 96% U238. If we consider the remainder a rounding error and assume all 60 tonnes is 60 million kg of U238. That will give us a very rough estimate of 3,000 m3.

Also worthy of noting are other wastes that comes from mining and refining.

There is much waste already. The “spent” waste is too radioactive to safely re-refine until later.

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