Mass defect (Δm)
Nuclear & Particle Physics - OCR A-Level Physics
Key Definition
Mass defect (Δm)
The difference between the total mass of the individual nucleons and the actual mass of the nucleus. Δm = Zm_p + (A-Z)m_n - m_nucleus.
The difference between the total mass of the individual nucleons and the actual mass of the nucleus. Δm = Zm_p + (A-Z)m_n - m_nucleus.
Key Definition
Binding energy
The minimum energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defect converted to energy via E = mc².
The minimum energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defect converted to energy via E = mc².
$$E = \Delta mc^2$$
$$E = \Delta m \cdot c^2$$
- 1 atomic mass unit (u) = 1.661 × 10⁻²⁷ $kg = 931.5 MeV/c^{2}$.
- A higher binding energyThe capacity to do work. Measured in joules (J). per nucleonThe binding energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c². of a nucleus divided by its nucleon number (mass number). Higher values indicate greater nuclear stability. means a more stable nucleus.
- Iron-56 has the highest binding energy per nucleonThe binding energyThe energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c². of a nucleus divided by its nucleon number (mass number). Higher values indicate greater nuclear stability. (≈ 8.8 MeV) - it is the most stable nucleus.
- The mass of a nucleus is always less than the sum of its parts. The 'missing' mass has been converted to binding energyThe energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c²..
Common Mistake
MEDIUM
Wrong: Binding energy is the energy stored inside the nucleus.
Right: Binding energy is the energy that must be supplied TO the nucleus to separate it. It is the energy released when the nucleus was formed. A nucleus with high binding energy is more stable, not more energetic.
Right: Binding energy is the energy that must be supplied TO the nucleus to separate it. It is the energy released when the nucleus was formed. A nucleus with high binding energy is more stable, not more energetic.