All subjects · Physics · WPH15 (Unit 5)

Fission, fusion and the binding energy curve

Both splitting heavy nuclei and joining light ones release energy. The binding energy per nucleon curve explains why, and why fusion is so hard to achieve.

Reading the curve

On a graph of binding energy per nucleon against nucleon number, the peak is near iron-56. Any nuclear change that moves nuclei towards the peak increases the binding energy per nucleon, so the products are more tightly bound and energy is released (the products have less mass).

Fission and fusion

Energy released = total binding energy of products - total binding energy of reactants, or c2 x (mass before - mass after).

Why fusion needs extreme conditions

Nuclei are positively charged and repel strongly. To get close enough for the strong nuclear force to act (about 10-15 m), they must collide at very high speeds, so the temperature must be very high (about 107 K or more). The density must also be very high, so collisions happen often enough to give a useful rate of fusion. In stars, gravity provides the high density and temperature.

Worked example

U-235 + n → Ba-141 + Kr-92 + 3n. Binding energies: U-235 1784 MeV, Ba-141 1174 MeV, Kr-92 783 MeV. Find the energy released.

  1. Free neutrons have no binding energy.
  2. Energy released = (1174 + 783) - 1784

Answer: 173 MeV

Key idea: Moving towards iron-56 on the BE per nucleon curve releases energy. Fusion needs high temperature (to overcome repulsion) and high density (for enough collisions).

Check yourself

  1. In a fission reaction, the products have total binding energy 1957 MeV and the uranium nucleus 1784 MeV. Find the energy released in MeV.
    Show answer

    173 MeV. Energy released = 1957 - 1784 = 173 MeV.

  2. Deuterium (2.014102 u) and tritium (3.016049 u) fuse to make helium-4 (4.002603 u) and a neutron (1.008665 u). Find the energy released, in units of 10-12 J, to 3 s.f.
    Show answer

    2.82 x 10-12 J. Δm = 5.030151 - 5.011268 = 0.018883 u = 3.13 x 10-29 kg; ΔE = 9.00 x 1016 x 3.13 x 10-29 = 2.82 x 10-12 J.

  3. Helium-4 has a total binding energy of 28.4 MeV. Find its binding energy per nucleon in MeV.
    Show answer

    7.1 MeV. 28.4 / 4 = 7.1 MeV per nucleon.

  4. Why does fusion need a very high temperature?
    • High temperatures make nuclei larger
    • The strong force only acts at high temperatures
    • Neutrons must be released first
    • Nuclei need very high kinetic energies to overcome their electrostatic repulsion
    Show answer

    Nuclei need very high kinetic energies to overcome their electrostatic repulsion. Only very fast nuclei get close enough for the strong force to take over.

  5. Why does fusion also need a very high density?
    • So the nuclei move faster
    • So collisions between nuclei are frequent enough
    • So the nuclei have less charge
    • So the binding energy decreases
    Show answer

    So collisions between nuclei are frequent enough. A higher density means more collisions per second, so a useful rate of fusion.

  6. Which nuclei can release energy by fission?
    • Nuclei lighter than iron-56
    • Only iron-56
    • Only hydrogen nuclei
    • Nuclei much heavier than iron-56
    Show answer

    Nuclei much heavier than iron-56. Splitting a heavy nucleus moves the products towards the peak of the curve.

  7. Why does iron-56 not release energy by either fission or fusion?
    • It has no neutrons
    • It has (close to) the highest binding energy per nucleon
    • It is radioactive
    • It has the lowest binding energy per nucleon
    Show answer

    It has (close to) the highest binding energy per nucleon. Any change would move it away from the peak, needing energy rather than releasing it.

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Last updated 7 November 2026. Spotted a mistake? Tell us.