Mass-energy equivalence (ΔE = Δmc²), nuclear fission and fusion with equations, the chain reaction, and balanced arguments for and against nuclear power.
Einstein showed that mass and energy are equivalent. A small loss of mass () in a nuclear reaction releases an enormous amount of energy ():
where m s⁻¹ is the speed of light. Even a tiny mass deficit produces a very large amount of energy because is enormous ( m² s⁻²).
The mass deficit is the difference between the total mass of the reactants and the total mass of the products. The products weigh slightly less than the reactants; the missing mass has been converted to energy.
Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei (fission fragments), releasing energy and several neutrons. The classic example is the fission of uranium-235:
Key points:
Each fission event releases 3 neutrons. If each neutron causes another fission, the number of fissions doubles each generation, a chain reaction. An uncontrolled chain reaction releases energy explosively (atomic bomb). In a nuclear reactor, control rods (usually boron or cadmium) absorb excess neutrons to keep exactly one neutron per fission causing the next, maintaining a controlled, self-sustaining chain reaction.
In the fission of U-235:
Suppose the total mass of reactants (U-235 + 1 neutron) is kg and the total mass of products (Ba-141 + Kr-92 + 3 neutrons) is kg.
Mass deficit:
Energy released:
This is the energy released per fission event, an enormous amount per kilogram of fuel compared to chemical reactions.
Nuclear fusion is the combining of light nuclei to form a heavier nucleus, releasing even more energy per unit mass than fission. The Sun's energy comes from fusion, four hydrogen nuclei combine to form helium:
A simpler fusion reaction studied for power generation:
Fusion requires extremely high temperatures (millions of degrees Celsius) to overcome the electrostatic repulsion between positively charged nuclei. At these temperatures, matter exists as a plasma. Achieving and containing fusion reactions long enough to generate net power is an ongoing research challenge.
| For | Against |
|---|---|
| Very large amounts of energy from a small mass of fuel | High construction and decommissioning costs |
| Low greenhouse gas emissions during operation | Risk of catastrophic accidents (Chernobyl 1986, Fukushima 2011) |
| Reliable base-load power generation (unaffected by weather) | Long-lived radioactive waste requires safe storage for thousands of years |
| Reduces dependence on imported fossil fuels | Uranium mining has environmental and safety impacts |
| No CO₂ during operation, helping limit global warming | Nuclear plants are targets for sabotage or terrorism |
Nuclear power is not currently used in the Caribbean, but the arguments above are examinable.
In mass-energy calculations: the mass deficit () is always LHS mass minus RHS mass (reactants minus products). If is positive, energy is released. Substitute in kg and use m s⁻¹ to get energy in joules.
For fission equations: check that A and Z balance on each side. The atomic number of Kr is 36, not 56 (which is Ba). A common exam error is confusing the identity of the products.