Fission, Fusion, and Nuclear Decay

Nuclear reactions conserve nucleon number and charge but not mass: the products of an energy-releasing reaction are lighter, and the defect leaves as energy through $E = \Delta mc^2$, with $1$ u corresponding to about $931$ MeV. Stability is ranked by binding energy per nucleon, which peaks near iron at roughly $8.8$ MeV, so moving toward that peak from either side releases energy, which is why fission works for heavy nuclei and fusion for light ones. Each half-life removes half of what remains rather than a fixed amount, and the half-life is fixed by the isotope alone.

Four errors dominate. Balancing masses across a reaction the way nucleon numbers balance, which reports zero energy released or reverses its sign. Ranking nuclei by total binding energy rather than by binding energy per nucleon, which makes uranium look most stable and makes both fission and fusion look like processes that should cost energy. Removing a fixed amount each half-life, so two half-lives leave nothing. And treating the half-life as depending on how much material is present or how long it has already sat.