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Asked in RS Academy GUJCET booklet · Energy released in fission and fusion
Given: the binding energy per nucleon is x for ⁿ_ZP, which has n nucleons, and y for ²ⁿ_Z'Q, which has 2n.
Idea: the energy released is the total binding energy of the product minus the total binding energy of the reactants. A nucleus's total binding energy is its binding energy per nucleon times its own number of nucleons.
Before: two P nuclei, 2× nx=2nx.
After: one Q nucleus, 2n× y=2ny.
Energy released =2ny-2nx=2n(y-x).
So energy is given out only when y>x, that is when the heavier product is the more tightly bound nucleus — which is exactly the condition for fusion to be worth anything.
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