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Although superficially nuclear power seems independent from solar energy, it in fact relies very much on conventional sources of energy. Uranium-235 is one possible fuel for nuclear power that is found naturally, but it is very scarce, and no nuclear power plants currently use it. They use plutonium-239, which must be manufactured by bombarding uranium with electrons; as you might imagine, this requires an energy source. Energy derived from chemical reactions is not feasible, because you would either need an enormous amount of raw material, or you would need to synthesize special heat-producing compounds, the creation of which requires energy.