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Can someone decipher what this means. I know that mass defect of the nucleus is equivalent to the binding energy but what does the rest of the sentence mean?
Edit: Is it saying that mass defect <=> Binding energy of products - Binding energy of reactants?
You could say it like that but remember they're different units. It's a bit ambiguous imo because I feel like no one points this out but when you compare the weight of constituent nucleons (broken up into individual protons and neutrons) to the actual mass of the nucleus, the former outweighs the latter. We aren't given really a reason why this occurs (could have to do with gluons and strong force perhaps) but the consequence is that this mass defect i.e. the difference of mass is converted into the binding energy that holds nucleus together. Now in relation to the statement. You can easily swap the 'binding energy gain' and 'mass defect' i.e. how much mass was lost in the reaction and converted into energy according to E=mc^2.
Say for example reactant A has 1u and reactant B has 2u mass and they form product C with 1.5u. The mass defect here is (1+2) - 1.5 = 1.5u. Convert this into MeV by timsing by 931.5 and you get the 'binding energy gain' of the product.
Since the mass defect of the product (1.5u + previous mass defect) is greater than the mass defect of the reactants (not given but inferred), there is 'binding energy gain' in the daughter nucleus
TL;DR 'binding energy gain' is mass defect (mass difference) between product and reactants, while binding energy is mass defect (difference between constituent mass and actual mass) of individual nuclei.