Properties of Nuclei and the Nuclear Force
Nuclear radius grows with the cube root of nucleon number, so nuclear density is nearly constant, and the force holding nucleons together is short ranged and blind to charge. Those two facts shape the binding energy curve.
What a learner can do afterwards
- Estimates a nuclear radius and density from the nucleon number
- Describes the range and charge independence of the strong force
- Explains why the binding energy per nucleon peaks near iron
1 · Read
A nucleus packs Z protons and N neutrons, with A the total, into a radius near 1.2 fm times the cube root of A. Carbon 12 holds 6 protons and 6 neutrons. Since volume grows with A, every nucleus shares nearly the same enormous density.
The strong force grips across a few femtometers, then fades and lets electric repulsion rule. It holds protons and neutrons almost equally, which mirror nuclei confirm: swap the counts and the binding barely changes. Light nuclei match protons with neutrons, while heavy ones past Z 15 carry extra neutrons as dilution against proton repulsion.
Try A equals 8. Its cube root is 2, so the radius is about 2.4 fm. Binding energy per nucleon climbs with size to a peak near iron, then falls, so light nuclei gain by fusing and heavy ones by splitting.
Read the curve, not just the size: the most tightly bound nuclei sit near the iron peak, and that is where fusion stops paying and fission starts.
Density stays flat, the force stays short and charge blind, and binding per nucleon peaks near iron.
More to read
10.1 Properties of Nuclei
Nuclei are tiny and dense beyond everyday intuition. The radius grows as the cube root of the nucleon number, about 1.2 femtometers times A to the one third. That scaling means volume is proportional to nucleon count, so every nucleus packs nearly the same density. A teaspoon of nuclear matter would outweigh a mountain.
21.1 Nuclear Structure and Stability
The strong force beats proton repulsion but only at arm length, fading within a few femtometers. It also treats protons and neutrons nearly alike, a property called charge independence. Each nucleon therefore binds only to its close neighbors instead of the whole nucleus. That saturation is why binding grows with volume while the surface pays a penalty.
10.2 Nuclear Binding Energy
Binding energy per nucleon rises steeply for light nuclei, tops out near iron, then slowly declines. The curve explains both fusion and fission: move toward iron from either side and the difference is released as energy. Stars burn upward to iron and stop, and heavy nuclei split downward toward it. Iron sits at the bottom of the nuclear energy valley.
2 · Watch
Take it off screen
Where it sits
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.