Nuclear reactions release enormous energy because the mass of a nucleus is not simply the sum of the masses of its separate protons and neutrons. The difference is called the mass defect, and it is linked to the energy that binds the nucleus together. Einstein's equation E = mc² explains why even a tiny amount of missing mass corresponds to a huge amount of energy.
This idea powers the Sun, nuclear reactors, and the energy released in nuclear weapons.
Key Facts
- Mass defect: Δm = mass of separate nucleons - mass of nucleus
- Energy from mass: E = Δmc²
- Speed of light: c = 3.00 × 10^8 m/s, so c² = 9.00 × 10^16 m²/s²
- Binding energy is the energy needed to separate a nucleus into individual protons and neutrons.
- In fission, a heavy nucleus splits into smaller nuclei and energy is released if total mass decreases.
- In fusion, light nuclei combine into a heavier nucleus and energy is released if the final nucleus has greater binding energy per nucleon.
Vocabulary
- Mass defect
- The mass defect is the difference between the mass of separate nucleons and the actual mass of the nucleus they form.
- Binding energy
- Binding energy is the energy required to pull a nucleus apart into its individual protons and neutrons.
- Nucleon
- A nucleon is a proton or neutron found in an atomic nucleus.
- Fission
- Fission is a nuclear process in which a heavy nucleus splits into smaller nuclei, often releasing neutrons and energy.
- Fusion
- Fusion is a nuclear process in which light nuclei combine to form a heavier nucleus, releasing energy when the products are more tightly bound.
Common Mistakes to Avoid
- Using the total mass instead of the mass defect: E = mc² uses the change in mass, not the entire mass of the original nucleus, when calculating released nuclear energy.
- Forgetting to convert atomic mass units to kilograms or MeV: units must match the form of the equation, such as 1 u = 1.6605 × 10^-27 kg or 1 u = 931.5 MeV/c².
- Assuming mass is destroyed: mass is converted into other forms of energy, so mass-energy is conserved even though rest mass decreases.
- Thinking fission and fusion release energy for the same structural reason: fission releases energy for very heavy nuclei, while fusion releases energy for light nuclei because both move products toward higher binding energy per nucleon.
Practice Questions
- 1 A nuclear reaction has a mass defect of 2.00 × 10^-29 kg. Calculate the energy released in joules using E = Δmc² with c = 3.00 × 10^8 m/s.
- 2 A fission event loses 0.215 u of mass. Calculate the energy released in MeV using 1 u = 931.5 MeV/c².
- 3 Explain why both splitting a uranium nucleus and fusing hydrogen nuclei can release energy, even though one process breaks a nucleus apart and the other builds one.