Mass-energy equivalence explains why tiny changes in mass can correspond to enormous amounts of energy. In nuclei, the mass of a bound nucleus is slightly less than the total mass of its separate protons and neutrons. This missing mass is called the mass defect, and it becomes nuclear binding energy through E = mc².
Understanding this idea helps explain nuclear power, stars, radioactive processes, and the stability of atoms.
Key Facts
- Mass-energy equivalence: E = mc², where c = 3.00 × 10^8 m/s.
- Mass defect: Δm = mass of separate nucleons - mass of bound nucleus.
- Binding energy: BE = Δmc².
- Binding energy per nucleon: BE/A, where A is the total number of protons and neutrons.
- Nuclei near iron and nickel have the highest binding energy per nucleon and are among the most stable.
- Fusion releases energy when light nuclei combine, while fission releases energy when very heavy nuclei split, because both move products toward higher binding energy per nucleon.
Vocabulary
- Mass-energy equivalence
- The principle that mass and energy are related by E = mc², so a small amount of mass can be converted into a large amount of energy.
- Mass defect
- The difference between the mass of a nucleus and the total mass of the separate protons and neutrons that form it.
- Binding energy
- The energy required to completely separate a nucleus into its individual protons and neutrons.
- Binding energy per nucleon
- The average binding energy for each proton or neutron in a nucleus, found by dividing total binding energy by the mass number.
- Nuclear stability
- A measure of how strongly a nucleus is held together and how unlikely it is to change through radioactive decay or nuclear reaction.
Common Mistakes to Avoid
- Confusing mass defect with lost matter, because the mass is not destroyed but appears as binding energy according to E = mc².
- Thinking higher total binding energy always means greater stability, because stability is better compared using binding energy per nucleon.
- Assuming only fission releases nuclear energy, because fusion of light nuclei also releases energy when products are more tightly bound.
- Using grams directly in E = mc², because the mass must be in kilograms when calculating energy in joules.
Practice Questions
- 1 A nuclear reaction has a mass defect of 2.0 × 10^-29 kg. Using c = 3.00 × 10^8 m/s, calculate the energy released in joules.
- 2 A nucleus has a total binding energy of 127.6 MeV and contains 16 nucleons. Calculate its binding energy per nucleon.
- 3 Explain why both the fusion of hydrogen into helium and the fission of uranium can release energy even though they are opposite processes.