Why are some nuclei more stable than others, and what holds a nucleus together?
Explain nuclear binding energy and the stability of nuclei using the binding-energy curve
A focused answer to the WACE Year 12 Physics Unit 4 content point on nuclear stability. The strong nuclear force, mass defect and binding energy, binding energy per nucleon, the shape of the binding-energy curve, and why fission and fusion release energy.
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What this dot point is asking
WACE wants you to explain what holds the nucleus together, define binding energy and binding energy per nucleon, and use the binding-energy curve to explain why fission and fusion release energy. This ties mass-energy equivalence to nuclear stability.
The strong nuclear force
Protons in a nucleus repel each other electrostatically, yet nuclei hold together. The strong nuclear force, attractive and far stronger than the electrostatic force but acting only over very short ranges (about the size of a nucleus), binds protons and neutrons (nucleons) together. Neutrons add this binding without adding repulsion, which is why heavier stable nuclei need more neutrons than protons.
Mass defect and binding energy
The mass of a nucleus is less than the total mass of its separate nucleons. This mass defect corresponds to the binding energy, the energy that would be needed to pull the nucleus apart into free nucleons:
Equivalently, this energy was released when the nucleus formed. A larger binding energy means a more tightly bound nucleus.
Binding energy per nucleon
Total binding energy grows with nucleus size, so to compare stability fairly we use the binding energy per nucleon,
where is the number of nucleons. This is the better stability measure: the higher it is, the more energy holds each nucleon and the more stable the nucleus.
The binding-energy curve
Plotting binding energy per nucleon against mass number gives a curve that rises steeply for light nuclei, peaks around iron and nickel (mass number near ), then declines slowly for heavy nuclei. Iron-region nuclei are the most stable. Any reaction that moves nuclei toward this peak releases energy, because the products are more tightly bound than the reactants.
Linking to fission and fusion
Heavy nuclei such as uranium lie to the right of the peak, so splitting them (fission) moves the fragments up toward the peak and releases energy. Light nuclei such as hydrogen isotopes lie to the left, so joining them (fusion) also moves toward the peak and releases energy. Both processes increase binding energy per nucleon, which is the unifying reason they are energy sources.
Comparing nuclei
To judge which of two nuclei is more stable, compare binding energy per nucleon, not total binding energy. A large nucleus can have a big total binding energy yet a lower per-nucleon value, making it less stable than a small, tightly bound nucleus.