True, the fission of Uranium in core reactors is induced fissioned, I shouldn't have used the phrase induced fission for separating the nucleus into its constituents.
1) if the fission is a decay process happening naturally without any energy being supplied to the nucleus (bombarding the nucleus with a neutron can be neglected), in which the initial nucleus is separated into two or more nuclei, and not its constituents, then energy is released in the process because the product nuclei have a greater binding energy. The energy released results in a decrease in mass of the products compared to the initial nuclei.
• if the fission is a process in which a nucleus, He-4 for example, is separated into its constituents, that is 2 protons and 2 neutrons all separated from each other then energy equal to the binding energy of nucleus, or He-4 for our example, must be supplied to the nucleus to separate it into its constituent protons and neutrons. Because the energy was supplied (assuming that there was no energy dissipation), this energy which has an equivalent mass that is stored in the constituent protons and neutrons ( note that the initial nucleus no longer exits for its mass to be greater than its constituents because the initial nucleus has already fragmented into its constituents). Therefore the mass of the initial nucleus < the mass of its constituent protons and neutrons.
2) you mentioned a very good point there. Comparing the mass of a He-4, for example, with its constituent protons and neutrons, with the constituents not being the product of fission of the He-4 nucleus you would still find that the mass of the He-4 is less than the mass of its constituents, thats the mass of 2 protons and 2 neutrons all separated from each other. This is because neutrons and protons separated from each other are in a higher energy state than when they are joined together. When they join energy is released in the process and so protons and neutrons ( constituents of all nuclei) have a greater mass than when they are joined because they have a greater energy content when separated.
3) that's true. In fusion the mass of the nucleus formed is less than the total mass of the initial nuclei but this is because energy is released when the initial nuclei joined together. Since energy has mass this means that mass was released from the initial nuclei during fusion and so the mass of the product nucleus will be less than the total mass of the initial nuclei.
In sum:
in fission( decay process):
Mass of initial nucleus > mass of the product nuclei
( fission happening naturally never results is breaking the nucleus into its constituents but only results in the formation of two or more smaller nuclei)
In fission ( breaking a nucleus into its constituents):
Mass of the initial nuclei < mass of the constituents of the nucleus
In fusion :
Mass of the initial nuclei > mass of the product nuclei.
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