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What is the difference between nuclear fusion and nuclear fission?

Very simply, fission splits a massive element into fragments, releasing energy in the process. Fusion joins two light elements, forming a more massive element, and releasing energy in the process. The reason they both release energy can be understood by examining a curve called the binding energy per nucleon curve. Since I cannot draw the curve for you here, I suggest you look it up. Basically, the significance of the curve is that it has an initial steep increase in binding energy per nucleon as the number of nucleons increases, reaches a maximum value, and then decreases gradually as the number of nucleon increases. In fission, an element with a very large number of nucleons (such as Uranium) is split, forming two fragments which each have fewer nucleons (the total number of nucleons is always constant). These fragments are nearer the maximum of the curve, so the total binding energy increases. In fusion, very light atoms (before the maximum of the curve) are fused into a more massive atom, neare the maximum again.

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