explain the relevance of binding energy per nucleon to nuclear reactions, including nuclear fusion and nuclear fission

What is mass defect?

When protons and neutrons (nucleons) stick together to form a nucleus, the total mass of the nucleus is a little *less* than the sum of the masses of the individual nucleons. That missing mass is called the mass defect (Δm). It is converted into binding energy that holds the nucleus together.

Think of nucleons as Lego bricks. When you snap them together, a little bit of the bricks’ mass “disappears” because the bricks are now glued together more tightly – that’s the mass defect.

Binding energy per nucleon

The binding energy per nucleon is the average energy that keeps each nucleon in the nucleus. It is calculated as:

\$\text{BE per nucleon} = \frac{\Delta m \, c^2}{A}\$

Where A is the mass number (total nucleons). A higher value means a more tightly bound nucleus.

Why does it matter for nuclear reactions?

• Energy can be released when a nucleus moves to a state with a higher binding energy per nucleon.
• Energy can be absorbed when a nucleus moves to a state with a lower binding energy per nucleon.
• Fusion: light nuclei combine to form a heavier nucleus with higher BE per nucleon → energy released.
• Fission: heavy nucleus splits into lighter nuclei with higher BE per nucleon → energy released.

Binding energy chart (MeV per nucleon)

Fusion vs. Fission – the energy story

Fusion (e.g., \$^1\$H + \$^1\$H → \$^4\$He) moves from low BE per nucleon (0) to higher (≈7 MeV). The difference is released as energy. This is how the Sun shines. 🌞

Fission (e.g., \$^{235}\$U → \$^{140}\$Xe + \$^{94}\$Kr) splits a heavy nucleus into two lighter ones with higher BE per nucleon (≈7.5 MeV). The energy difference powers nuclear reactors. ⚡

Both processes involve moving toward the peak of the binding‑energy curve (around iron). The closer you get to the peak, the more energy you can release.

Exam tip box 📚

1. Remember the binding‑energy curve – peak at iron.
2. Use the formula ΔE = Δm c² to calculate energy released.
3. When comparing fusion and fission, look at the change in BE per nucleon.
4. For reaction questions, sketch the curve and mark initial and final points.
5. Always state whether energy is released (exothermic) or absorbed (endothermic).