Binding energy per nucleon – the curve, fission and fusion
PhysicsQuantum & Nuclear PhysicsAges 17–18
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Quantum & Nuclear Physics
A graph of binding energy per nucleon Eb/A against mass number A, built from real masses of about 30 nuclei from ²H to ²³⁸U, with its peak around ⁵⁶Fe – ⁶²Ni. Select a nucleus to see Z, N, the mass defect Δm, Eb = Δm·c² and Eb/A. Animations of ²³⁵U fission and D + T fusion show about 200 MeV and 17.6 MeV being released because the products sit higher on the curve.
Lesson: Nuclear binding energy, nuclear fission and fusion
What it shows
The mass of a nucleus is less than the total mass of its separate protons and neutrons. This mass defect Δm = Z·mp + N·mn − mX corresponds to the binding energy Eb = Δm·c², the energy needed to pull the nucleus apart into free nucleons (1 u·c² = 931.5 MeV). Plotting Eb/A against mass number gives a curve that rises steeply for light nuclei, peaks near iron and nickel, then falls slowly for heavy nuclei. Any reaction whose products lie higher on the curve releases energy: fusion of light nuclei and fission of heavy ones.
How to use
Tap a point on the graph or choose a nucleus from the Nucleus list to read Z, N, the nuclear mass, Δm, Eb and Eb/A, and compare light, middle and heavy nuclei. Then press ²³⁵U fission to watch a slow neutron split uranium into ¹⁴¹Ba, ⁹²Kr and three neutrons, and D + T fusion to watch deuterium and tritium form ⁴He and a neutron. Compare the energy released per nucleon in the two reactions.
Parameters you can change
- Selected nucleus ²H (deuterium), ⁴He, ¹²C, ¹⁶O, ⁵⁶Fe, ⁶²Ni, ²⁰⁸Pb, ²³⁵U, ²³⁸U
- Reaction shown ²³⁵U fission, ²H + ³H fusion, None, just view the nucleus
- Label nuclei on the graph
Questions to explore
- Why is ⁵⁶Fe more stable than both ⁴He and ²³⁵U, even though ²³⁵U has a larger total binding energy?
- Using the binding energies shown, how much energy is released when ²³⁵U splits into ¹⁴¹Ba and ⁹²Kr?
- How does the energy released per nucleon in D + T fusion compare with that in ²³⁵U fission?
