Nuclear energy: mass-energy equivalence, the mass defect and binding energy, binding energy per nucleon, and the energy released in nuclear fission and fusion.

Energy from mass-energy equivalence: $E = \Delta m\, c^2 = (3.0 \times 10^{-28})(3.0 \times 10^{8})^2 = (3.0 \times 10^{-28})(9.0 \times 10^{16}) = 2.7 \times 10^{-11}\ \text{J}$.

In MeV: $E = \dfrac{2.7 \times 10^{-11}}{1.6 \times 10^{-13}} = 169\ \text{MeV}$.

In a reactor this energy appears mostly as kinetic energy of the fission fragments, which is transferred to the surrounding material as heat; the heat boils water to drive a turbine and generate electricity.

Markers reward $E = \Delta m c^2$, the conversion to about $169\ \text{MeV}$, and identifying the energy as heat used to generate electricity.

The binding energy per nucleon curve rises steeply for light nuclei, peaks near iron-56 (the most stable nuclei), then falls slowly for heavy nuclei. A higher binding energy per nucleon means a more tightly bound, more stable nucleus.

In fission, a heavy nucleus (such as uranium) splits into medium nuclei that lie closer to the iron peak, so they have a higher binding energy per nucleon. This increase in binding energy is released.

In fusion, light nuclei (such as hydrogen isotopes) combine into a slightly heavier nucleus higher up the steep part of the curve, again increasing the binding energy per nucleon and releasing energy.

Markers reward describing the curve (peak near iron-56), and explaining that both processes move nuclei towards the peak, increasing binding energy per nucleon and releasing energy.