Physics · nuclei · NEET
Energy release does not depend on joining or breaking. It depends only on whether the products are MORE tightly bound than the reactants. For light nuclei, the fused product sits higher on the binding energy per nucleon curve, so the nucleons end up more tightly bound. That extra binding energy is released. So both fusion (of light nuclei) and fission (of heavy nuclei) can release energy, because both move the system toward the tightly-bound middle of the curve.
Fusion of light nuclei INCREASES the binding energy per nucleon. For example, hydrogen isotopes have only about 1 to 3 MeV per nucleon, but helium-4 has about 7 MeV per nucleon. When two light nuclei fuse and the value goes up, the difference is given out as energy. This is exactly why the reaction is exothermic (releases energy).
It comes from a tiny loss of mass. The total mass of the final nucleus is slightly LESS than the total mass of the starting nuclei. This missing mass is called the mass defect (delta m). It converts to energy using Einstein's relation E = (delta m) c^2. In nuclear units, 1 u of mass defect gives 931.5 MeV of energy. So the released energy = (mass defect in u) x 931.5 MeV.
Look at the binding energy curve. For light nuclei (A less than 30) the curve rises very steeply. So fusing two light nuclei moves them up a big jump, giving a large energy gain per nucleon. Heavy nuclei are already near the flat top of the curve, so fusing them would gain little or even cost energy. That is why the Sun uses hydrogen (very light) as fuel, not heavy elements.
Mass is LOST. The final nucleus weighs slightly less than the sum of the reactant masses. This lost mass is the mass defect, and it is not destroyed, it is converted into energy. Nothing violates conservation, because mass and energy together are conserved through E = mc^2.
Both nuclei are positively charged, so they repel each other by the Coulomb force. To get close enough for the short-range attractive nuclear force to act, they need very high kinetic energy, which means very high temperature (around 10^8 K in stars). Once they fuse, the released nuclear energy is far larger than the input energy needed to overcome the Coulomb barrier. So the reaction is still net energy-releasing.
Because the fused nucleus has higher binding energy per nucleon, so nucleons become more tightly bound and the lost mass (mass defect) turns into energy via E = mc^2.
Find the mass defect: delta m = (total mass of reactants) minus (total mass of products), in atomic mass units u. Then energy released Q = (delta m) x 931.5 MeV. A positive Q means energy is released.
Two deuterons fusing: (deuterium-2) + (deuterium-2) gives helium-3 + a neutron, releasing about 3.27 MeV. Another: deuterium-2 + tritium-3 gives helium-4 + neutron, releasing about 17.6 MeV.
The binding energy curve rises very steeply for light nuclei, so fusing them gives a big jump in binding energy per nucleon. Fission of heavy nuclei moves along the flatter part, so per-nucleon fusion energy can be larger.
Yes, in stars including our Sun. Hydrogen nuclei fuse into helium through the proton-proton cycle, and this is the main energy source of stars.
