Apply mass-energy equivalence to rest energy and to the mass defect and energy release in nuclear processes.

What this dot point is asking

You need to apply $E = mc^2$ to calculate rest energy, and to relate the mass defect in a nuclear process to the energy released.

Mass and energy are the same thing

Einstein's special relativity shows that mass is a highly concentrated form of energy. Even an object at rest possesses energy purely because it has mass.

This does not mean ordinary objects easily release this energy. In chemical reactions the mass change is far too small to detect. It is only in nuclear reactions that a measurable fraction of mass is converted.

Mass defect and binding energy

The mass of a nucleus is slightly less than the total mass of its individual protons and neutrons. This difference is the mass defect, and the equivalent energy is the binding energy that holds the nucleus together.

In any nuclear reaction (fission, fusion or radioactive decay), if the products are more tightly bound than the reactants, the surplus mass is released as kinetic energy of the products and radiation.

Fission, fusion and the Sun

• Fission splits a heavy nucleus (like uranium-235) into lighter fragments that are more tightly bound; the mass defect appears as energy. This powers nuclear reactors.
• Fusion joins light nuclei (like hydrogen isotopes) into a more tightly bound nucleus (helium). The Sun fuses hydrogen into helium, converting about 4 million tonnes of mass into energy every second.

Both release energy because the products sit higher in binding energy per nucleon than the reactants. The binding-energy-per-nucleon curve peaks near iron, so nuclei lighter than iron release energy by fusing toward it, while nuclei heavier than iron release energy by splitting toward it. This single curve explains why fusion powers stars but fission powers reactors: each process moves nuclei toward the more tightly bound middle of the curve, releasing the surplus mass as energy.

How SACE assesses this

SACE Stage 2 questions almost always supply rest masses (often in kilograms) and ask for the energy released by annihilation, the energy from a stated mass defect, or the frequency of an emitted photon. Quote $E = mc^2$ before substituting, keep the factor $c^2 = 9.00\times10^{16}$ explicit, and when two photons are produced remember to halve the total energy before applying $E = hf$. Finishing with a sentence in context, such as identifying the radiation region, secures the communication marks.

Energy can also create mass

The equivalence works both ways. In particle accelerators, kinetic energy can be converted into new particles with real mass, and in pair production a photon can create an electron-positron pair. Mass-energy together is conserved, even though neither alone always is. Annihilation, as in the PET-scan question above, is the reverse process: mass becomes pure photon energy.