Mass–energy equivalence
Einstein showed that mass and energy are equivalent. In a nuclear reaction a tiny mass defect (Δm) — the difference between the total mass before and after — is converted into a large amount of energy.
Key formula / 关键公式
Energy released:
E = mc²
where m = mass lost (kg) and c = speed of light = 3.0 × 10⁸ m s⁻¹. Because c² is huge, even a tiny mass releases enormous energy.
Fission and fusion
- Nuclear fission: a large nucleus (e.g. uranium-235) splits into two smaller nuclei when hit by a neutron, releasing energy and more neutrons that can cause a chain reaction. Used in nuclear power stations.
- Nuclear fusion: two light nuclei (e.g. hydrogen isotopes) join to form a heavier nucleus, releasing even more energy per kilogram. This is the source of the Sun's energy.
Worked example / 例题
In a reaction the mass defect is 3.0 × 10⁻²⁸ kg. Find the energy released.
E = mc² = (3.0 × 10⁻²⁸)(3.0 × 10⁸)² = (3.0 × 10⁻²⁸)(9.0 × 10¹⁶) = 2.7 × 10⁻¹¹ J.
Uses and hazards
Nuclear power generates large amounts of electricity from little fuel and produces no carbon dioxide, but creates radioactive waste and carries the risk of leaks. Safe handling, shielding and proper waste storage are essential.
Remember / 记住
- Energy comes from lost mass: E = mc².
- Fission splits a heavy nucleus; fusion joins light nuclei.
- c = 3.0 × 10⁸ m s⁻¹, so a small mass gives huge energy.