--- title: "Mass Defect and Binding Energy per Nucleon" description: "A bound nucleus has less rest mass than its separate protons and neutrons. This mass defect corresponds to its binding energy through E = mc squared. Binding energy per nucleon reaches its highest reg" canonical: https://lightmysky.com/learn/science/mass-defect-and-binding-energy-per-nucleon-mt_UdYE8hgXyl source: https://lightmysky.com/learn/science/mass-defect-and-binding-energy-per-nucleon-mt_UdYE8hgXyl.md retrieved: 2026-11-12 --- > **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`. # Mass Defect and Binding Energy per Nucleon A bound nucleus has less rest mass than its separate protons and neutrons. This mass defect corresponds to its binding energy through E = mc squared. Binding energy per nucleon reaches its highest region near iron and nickel. Subject: Science · Area: Matter & Materials · Ages 17 to 18 Page: https://lightmysky.com/learn/science/mass-defect-and-binding-energy-per-nucleon-mt_UdYE8hgXyl ## Ready when they can - Calculates the mass defect and the binding energy of a stated nuclide - Calculates binding energy per nucleon and identifies the high-binding region near iron and nickel - Uses stated binding energies to determine whether a reaction with unchanged total protons and neutrons releases or requires energy ## Lesson: The missing mass that holds nuclei together You have used E = mc squared. A bound nucleus has less rest mass than its free protons and neutrons together. Mass defect = total free-nucleon mass minus nuclear mass. Binding energy is the energy needed for complete separation into free nucleons at rest. Nuclear masses exclude electrons. If using atomic masses, account for electrons consistently. **Example.** Suppose stated nuclear masses total 5000 MeV/c squared before binding and 4988 MeV/c squared after binding. The defect is 5000 - 4988 = 12 MeV/c squared. Binding energy = mass defect × c squared, so it is 12 MeV. Use the same mass units before subtracting. For a mass defect in u, multiply by 931.5 to obtain binding energy in MeV. Divide total binding energy by mass number, the number of nucleons, to find binding energy per nucleon. For example, a stated total of 18 MeV across 3 nucleons gives 6 MeV per nucleon. This is an average for complete separation, not the exact energy needed to remove a particular nucleon. *(drawing: Binding energy per nucleon in MeV. These selected values are not a curve plotted against mass number.)* The curve of binding energy per nucleon against mass number generally rises for light nuclei, peaks in the iron and nickel region, then falls for heavier nuclei. Iron-56 is near the maximum, not its unique highest point. There are local peaks. Nuclear attraction acts mainly between nearby nucleons. Electrical repulsion between protons acts over longer distances, helping explain the fall for heavy nuclei. For a reaction with unchanged total protons and neutrons, add the binding energies of all products and compare with all starting nuclei. A larger final total releases energy; a smaller one requires energy. With nucleon count conserved, compare nucleon-weighted averages too. Many light-nucleus fusion and heavy-nucleus fission reactions release energy, but the stated products decide. An energy-releasing reaction may still face a barrier. For breakup into stated fragments, subtract their total binding energy from the starting binding energy. A positive difference must be supplied. A nucleus bound by 20 MeV splitting into two fragments each bound by 3 MeV needs 20 - 2 × 3 = 14 MeV. Complete separation into free nucleons requires the whole binding energy. **Recap.** Convert mass defect to binding energy, divide by nucleon count, and compare total binding energies for the stated reaction. *Lesson, questions and flashcards written for this dataset. Physics references were consulted for facts and calculation methods.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Inside the Atom: the Nuclear Model](https://lightmysky.com/learn/science/inside-the-atom-the-nuclear-model-mt_B_PtnvyRIo) - [Mass, Energy and the Unified Atomic Mass Unit](https://lightmysky.com/learn/science/mass-energy-and-the-unified-atomic-mass-unit-mt_GTfhALD90X) ## Opens up - [Properties of Nuclei and the Nuclear Force](https://lightmysky.com/learn/science/properties-of-nuclei-and-the-nuclear-force-mt_HdMS_muGWa) - [Energy Released in Fission and Fusion](https://lightmysky.com/learn/science/energy-released-in-fission-and-fusion-mt_VrqLAATXQY)