Nuclear energy does not produce electricity on its own. The nuclear energy it produces is used to heat water . The hot water then turns to steam that is used to turn dynamo turbines. This is thermal energy turned to mechanical energy. The dynamo turbines turn the mechanical energy into electric energy.
Nuclear energy lasts longer because the same volume as compared to fossil fuels produced a larger magnitude of energy, million of magnitudes larger. Therefore with the controlled release of this enormous energy, nuclear energy can last much longer than fossil fuels.
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