Mass Defect and Binding Energy per Nucleon
A nucleus weighs less than its separate nucleons, and that missing mass is the energy it would take to pull it apart. Dividing by the number of nucleons gives the curve that peaks near iron.
What a learner can do afterwards
- Calculates the mass defect and the binding energy of a stated nuclide
- Divides by nucleon number and places the nuclide on the binding energy curve
- Reads the curve to say which changes release energy and which would absorb it
1 · Read
A nucleus weighs less than its separate parts. The mass defect is the mass of the free nucleons minus the mass of the whole nucleus. For the deuteron, proton 938.28 plus neutron 939.57 minus the bound 1875.61 leaves a defect of 2.24 MeV/c squared. That missing mass is the price of pulling it apart.
Turn the defect into energy with E equals m c squared. Helium-4 has a defect of 0.030378 u, and with 1 u worth 931.5 MeV this gives 28.3 MeV of binding energy. Divide by its 4 nucleons to get 7.075 MeV per nucleon, far above deuterium's 1.12.
Plot binding energy per nucleon against mass number and the curve rises, peaks very near iron-56, then tapers off. Values average about 8 MeV. At low mass each new nucleon bonds with all the rest, but past iron new protons feel every other proton's repulsion while the short range attraction stays capped.
Read the curve as a hill that pays you to climb it. Joining light nuclei below iron moves the product upward, so fusion frees energy. Splitting heavy nuclei above iron also moves the fragments upward, so fission frees energy. Iron itself sits at the top, the end of the line.
Missing mass measures binding energy, and the per-nucleon curve peaks at iron, ruling which changes pay out.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.