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How are nuclear fission and fusion compatible with the law of conservation of energy? During fission $He$ splits into 2 hydrogen atoms along with enormous amount of heat energy and hydrogen also combine to form helium with enormous amount of heat energy. But in my opinion to follow the law of conservation of energy one of the reactions must be endothermic. Please clear this vagueness.

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The energy released/absorbed in nuclear reactions depends on the binding energies of the nuclei.So yes,energy is released in nuclear fusion of hydrogen to helium while energy will be absorbed in the reverse fission reaction.The curve below illustrates this point precisely: enter image description here

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Looking at this graph you also can deduce that fusion process (taking place in star) will cook element up to iron and then stop as it is no more possible to gain energy doing fusion from iron. – floqui Aug 28 '13 at 13:11
As an amendment to @floqui's statement, it will be possible to endothermically produce elements heavier than iron in stars (particularly during supernovae), but these processes will not create net energy, but will rather consume energy produced by the fusion of lighter elements. – Jerry Schirmer Aug 28 '13 at 16:34

Short story: They aren't compatible.

The Law of Conservation of Energy, and its companion the Law of Conservation of Mass, are only approximations of the Law of Conservation of Mass/Energy. The approximations work because of the huge conversion factor, $c^2$, to go from mass to energy.

This means that in any chemical reaction, the "mass" of the energy involved is immeasurably small, compared to the mass of the chemicals taking part.

Look at any specific nuclear reaction (fission fusion, decay, etc) and measure the masses and kinetic energies of all the reagents and all the products. Convert the energies into masses using $c^2$, and the total mass/energy will be conserved!

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