Mass defect is the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons.
When nucleons bind together, a tiny amount of mass is lost and converted into energy according to Einstein’s famous equation:
\$E = \Delta m\,c^2\$
That lost mass is called the mass defect (\$\Delta m\$).
Binding energy per nucleon tells us how tightly each nucleon is held in the nucleus. It’s calculated as:
\$\frac{E_b}{A} = \frac{(\text{mass of nucleons} - \text{mass of nucleus})\,c^2}{A}\$
Higher values mean a more stable nucleus.
| Element | A (Mass Number) | Binding Energy per Nucleon (MeV) |
|---|---|---|
| Hydrogen (H) | 1 | 0.0 |
| Helium (He) | 4 | 7.07 |
| Carbon (C) | 12 | 7.68 |
| Iron (Fe) | 56 | 8.79 |
| Uranium (U) | 238 | 7.57 |
Fusion is like two Lego blocks snapping together to form a bigger block. When light nuclei (like hydrogen) combine, they form a heavier nucleus (like helium) and release energy.
Key equation:
\$\text{D} + \text{T} \rightarrow \, ^4\text{He} + n + 17.6\,\text{MeV}\$
💡 Why 17.6 MeV? It’s the difference in binding energy between the reactants and the product.
🔍 Exam Tip: Remember that fusion releases energy when binding energy per nucleon increases from reactants to product.
Fission is like splitting a big Lego block into two smaller blocks. Heavy nuclei (e.g., uranium-235) absorb a neutron, become unstable, and split into two lighter nuclei plus some neutrons.
Typical reaction:
\$^{235}\text{U} + n \rightarrow\, ^{140}\text{Xe} + ^{94}\text{Sr} + 3n + 200\,\text{MeV}\$
💡 The released energy comes from the higher binding energy per nucleon of the fission fragments.
🔍 Exam Tip: In fission questions, calculate the mass defect of the reactants and products to find energy released. Use \$E = \Delta m\,c^2\$.
Think of the binding energy curve as a hill:
✨ Final Exam Reminder: Always check whether the reaction moves towards or away from the peak of the binding energy curve. That determines if energy is released or absorbed.