Why does nuclear fusion give more energy than nuclear fission?

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It doesn’t, not atom per atom. As other answers to this question point out, a typical fission reaction releases about 200 MeV of energy. (If you don’t know what MeV means, don’t worry about that for now.)
A typical fusion reaction releases about 18 MeV. That’s less than 10% of the energy released by fission!
However, if you have equal weights of fuel, then the energy released by fusion is greater. That’s because one atom of U-235 has a mass of 235 nuclei, whereas the mass of D + T has the mass of 5 nuclei. That’s a factor of 47 less weight. So for equal weights of fuel, fusion releases more energy.
Here is a curious fact: in most US thermonuclear weapons, about half of the energy comes from fission! The fusion core emits a large number of fast neutrons, and these neutrons are capable of causing fission in ordinary U-238. So the fusion core in such a bomb is surrounded by U-238, and the induced fission gives about half of the energy. It also gives almost all of the fallout. So in the neutron bomb, this layer is omitted, resulting in much less fallout. The emitted neutrons, which can kill anyone nearby, give the neutron bomb its name.
If you are still concerned about what MeV means, it is a unit of energy that is very useful for nuclear reactions. It means “one million eV” where the eV (or “electron volt”) is an energy unit equal to 1.6 x10^-19 joules.

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