Why do nuclear power plants produce so much energy?

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If nuclear power plants boil water to turn a turbine to make energy then why do they make more energy than a coal power plant that does the same?

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In a coal or natural gas power plant you are extracting the energy from the chemical bonds holding the carbon and hydrogen atoms together by burning them.

In a nuclear power plant you are extracting the energy from the nuclear bonds holding the protons and neutrons of uranium atoms together by letting neutrons smash into the atoms.

There is rediculiously more energy in nuclear bonds than chemical bonds.

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