--- title: "Nuclear Models: the Liquid Drop and the Semi-Empirical Mass Formula" description: "Treating a nucleus as an incompressible charged drop gives volume, surface, Coulomb, asymmetry and pairing terms that reproduce the binding energy curve to within a per cent. The same formula says whi" canonical: https://lightmysky.com/learn/science/nuclear-models-the-liquid-drop-and-the-semi-empirical-mass-formula-mt_-cTGNdUJLz source: https://lightmysky.com/learn/science/nuclear-models-the-liquid-drop-and-the-semi-empirical-mass-formula-mt_-cTGNdUJLz.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Nuclear Models: the Liquid Drop and the Semi-Empirical Mass Formula Treating a nucleus as an incompressible charged drop gives volume, surface, Coulomb, asymmetry and pairing terms that reproduce the binding energy curve to within a per cent. The same formula says which nuclide in an isobaric chain is stable and why heavy nuclei fission at all. Subject: Science · Area: Quantum & Modern Physics · Ages 20 to 21 Page: https://lightmysky.com/learn/science/nuclear-models-the-liquid-drop-and-the-semi-empirical-mass-formula-mt_-cTGNdUJLz ## Ready when they can - Names each term of the mass formula and says what physical picture it comes from - Predicts the most stable nuclide for a fixed nucleon number and compares it with the chart of nuclides - Uses the formula to argue that fission of a heavy nucleus releases energy while fission of a light one does not ## Lesson: The nucleus as a charged drop Picture the nucleus as a drop of incompressible fluid with a sharp surface and uniform density. This works because nuclear density stays nearly constant and the force is short ranged. Weigh a nucleus and it comes out lighter than its separate protons and neutrons. The missing mass times c squared is the binding energy. Divide by the nucleon count to compare light and heavy nuclei fairly. Five terms share the binding. Volume pays for interior nucleons feeling full attraction. Surface subtracts for skin nucleons with fewer neighbours. Coulomb subtracts the proton repulsion, which grows with the square of their number while spreading over the radius. Asymmetry and pairing fine tune the total. Each term maps straight onto one picture in the drop. For a fixed nucleon number the formula is a parabola in charge, and the bottom of the curve is the most stable nuclide. Plot stability against proton and neutron numbers and you get the band of stability, with the chart of nuclides as the scoreboard. Compare your predicted minimum with that chart. Extra tough nuclei sit at magic numbers, like closed shells in atoms. **Tip.** The binding per nucleon climbs steeply, peaks near iron, then falls away, and that single shape decides which direction pays. Heavy nuclei gain per nucleon by splitting, so fission releases energy. Light nuclei gain by joining, so fusion releases energy there. Fission of a light nucleus would climb the wrong way and cost energy. **Recap.** Five drop terms reproduce the binding curve, the parabola bottom picks the stable nuclide, and the iron peak decides whether splitting or joining pays. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Properties of Nuclei and the Nuclear Force](https://lightmysky.com/learn/science/properties-of-nuclei-and-the-nuclear-force-mt_HdMS_muGWa) ## Opens up - [The Nuclear Shell Model and the Magic Numbers](https://lightmysky.com/learn/science/the-nuclear-shell-model-and-the-magic-numbers-mt_1tiXMm0sA2)