A bound nucleus weighs less than its loose parts. That missing mass — Aston's packing fraction, Einstein's E = mc² — is the energy that holds it together: B = (Z mp + N mn − M) c². Plotted per nucleon it rises to an iron summit near 8.8 MeV, and every reaction — fusion from below, fission from above — that climbs toward it releases energy. The blue team builds and defends the curve; the red team tries to break it.
source F. W. Aston — mass-spectrograph, isotopes & the whole-number rule (1920); the packing fraction is the mass defect per nucleon — with A. Einstein, E = mc² (Annalen der Physik, 1905). Aston, "Atoms and their Packing Fractions", Nature 120, 956 (1927). Rendered, not quoted. AMBER — no single open primary link; masses are CODATA/AME values.
Beneath the measured curve sits a model: Weizsäcker's semi-empirical mass formula, the nucleus as a charged liquid drop of five competing terms —
+ volume aVA − surface aSA2/3 − Coulomb aCZ(Z−1)/A1/3 − asymmetry aA(A−2Z)²/A ± pairing.
For the current nuclide, live term contributions (MeV):
| term | MeV | sign |
|---|
The mass that binds — Aston & Einstein. B = (Z mp + N mn − M) c² peaks near Fe-56 / Ni-62 at ~8.8 MeV/nucleon.
That summit is the hinge of two neighbours: the-nuclear-fusion climbs it from below (light nuclei), the-nuclear-fission descends to it from above (heavy nuclei). Both release the binding difference. Each sphere is the next one's premise.
The blue team's live check: recompute the deuteron, He-4, the iron peak, and both reaction directions from the real masses, and confirm the mass defect stays positive. If red tampers, this badge is where it shows.
To weigh a nucleus you need only three numbers: how many Z protons, how many N neutrons, and the measured mass M of the whole. The parts are known exactly:
| constant | value |
|---|---|
| proton mp | 1.007276 u |
| neutron mn | 1.008665 u |
| 1 u (= m c²) | 931.494 MeV |
| NA | 6.022×10²³ /mol |
Add the loose parts, subtract the measured whole: the difference is the mass defect. Feed it to the panel.
Mass defect ∆m = (Z mp + N mn) − M, then B = ∆m · c². The nucleus is lighter than its parts; that vanished mass is the binding.
Every value is computed on the spot from the tabulated mass — nothing is looked up. The curve is the real B/A of each plotted nuclide.
What the machine proves: the mass defect is real and positive for every bound nucleus (M < parts); the binding per nucleon rises from light nuclei, peaks near Fe-56 / Ni-62 at ~8.8 MeV, and declines for the heaviest — so fusing light and fissioning heavy both walk uphill, releasing energy.
The blue team's witness (left) confirms these numbers live; the red team (right) tries to make the defect lie.
And "mass converts to energy" is loose. The nucleons keep their identity; what changes is the potential energy of their binding — which we weigh as mass. The energy was never absent; it was hiding in the scale.
"Iron-56 is the most tightly bound nucleus." Cut. Ni-62 holds the record B/A (~8.795); Fe-56 is a hair below (~8.790). Iron dominates stellar ash for kinetic reasons, not because it is the summit.
"In fission the split neutron's mass becomes the energy." Cut. The energy is the difference in binding energy between the heavy nucleus and its more-bound fragments — the mass defect, not a vanished particle.
"Fusion runs all the way up in every star." Cut. Silicon burning stalls at the iron peak — beyond it fusion is endothermic; only the most massive stars reach it, and it triggers collapse, not more energy.
The red team's move: flip the sign — add the defect instead of subtracting, so the model claims the nucleus is heavier than its parts. The binding comes out negative; the witness (window 7) is watching.
Make M heavier than the loose parts and the mass defect goes negative — the nucleus would be unbound, would fly apart. The witness recomputes, sees B < 0, and turns red. Nothing is faked; the attack is real and it is caught.