What is mass defect and how does it relate to E = mc2?
Mass defect is the difference between the combined mass of a nucleus’s individual protons and neutrons and the actual measured mass of the bound nucleus. The bound nucleus always has slightly less mass than the sum of its separate nucleons. This “missing” mass has been converted into energy.
Mass defect is the “missing” mass converted into nuclear binding energy, explained by Einstein’s equation E = mc2
Einstein’s equation, E = mc2, explains this relationship. The lost mass (m) has been converted into binding energy (E), which holds the nucleus together. The larger the mass defect, the greater the binding energy and the more stable the nucleus.
Mass defect therefore provides a direct way to calculate nuclear binding energy and to understand why energy is released during radioactive decay.
Understanding the physics
When protons and neutrons bind together to form a nucleus, they move into a lower-energy state due to the strong nuclear force. Energy must be released during this process. Because mass and energy are equivalent, this released energy corresponds to a reduction in mass.
If we take the mass of all protons and neutrons separately and compare it to the mass of the nucleus they form, the nucleus weighs slightly less. That difference is the mass defect.
Mathematically:
Binding energy = (mass defect) x c2
where c is the speed of light. Since c2 is a very large number, even a tiny mass difference corresponds to a substantial amount of energy.
This principle explains why nuclear reactions can release large amounts of energy. In radioactive decay, a parent nucleus transforms into a daughter nucleus with greater binding energy per nucleon. The difference in binding energy is released as emitted electromagnetic or particulate radiation, such as gamma photons or kinetic energy of particles.
Mass defect therefore reflects how much energy is stored in the nuclear binding of a given isotope.
| Feature | Mass Defect | Binding Energy |
|---|---|---|
| Definition | The difference between the sum of the masses of individual nucleons and the actual mass of the nucleus | The energy required to completely separate a nucleus into its individual nucleons |
| Physical meaning | Represents the missing mass that has been converted into energy during nucleus formation | Represents the energy equivalent of the mass defect |
| Relationship between the two | Converted into energy via Einstein’s mass–energy relation | Calculated from the mass defect using (E = mc2) |
| Units | Atomic mass units (u) or kilograms | Electron volts (eV), typically MeV in nuclear physics |
| Formula | Mass defect = 𝑍𝑚𝑝 + 𝑁𝑚𝑛 −𝑚nucleus | Eb = Δmc2 |
| What it indicates | How much mass is lost when nucleons bind together | How strongly nucleons are bound within the nucleus |
| Implication for nuclear stability | Larger mass defect → more energy released during formation | Higher binding energy → more stable nucleus |
| Derived quantity | A mass difference measurement | An energy derived from the mass defect |
| Common exam concept | Used to calculate binding energy | Used to compare nuclear stability via binding energy per nucleon |
Where this matters clinically
Every radionuclide used in nuclear medicine releases energy because the daughter nucleus has a different binding energy configuration. For example, the gamma photons detected in imaging ultimately arise from differences in nuclear binding energy which is a direct consequence of mass–energy equivalence.
