Mass Defect and Nuclear Binding Energy
Why the nucleus has less mass than its parts
Mass defect
If you add up the masses of free protons and neutrons, the total is slightly larger than the actual mass of the bound nucleus. This difference is called the mass defect.
Binding energy
The missing mass has been converted into energy that holds the nucleus together. Using Einstein's relation , the binding energy is .
Energy and stability
A nucleus with larger binding energy per nucleon is generally more stable than one with smaller binding energy per nucleon.
Binding energy per nucleon
To compare nuclei of different sizes, physicists often divide the total binding energy by the number of nucleons, .
Concept summary
| Concept | Meaning |
|---|---|
| Mass defect | Difference between summed free-particle mass and actual nucleus mass |
| Binding energy | Energy needed to separate a nucleus into free nucleons |
| Binding energy per nucleon | Average binding energy for each nucleon in the nucleus |
What does mass defect mean?
The bound nucleus weighs slightly less than the separate nucleons because some mass appears as binding energy.
Correct answer: The nucleus has less mass than the sum of free nucleons
What formula relates binding energy to mass defect?
More precisely, .
Correct answer: E = mc^2
A nucleus with higher binding energy per nucleon is usually more
Higher binding energy per nucleon usually means the nucleons are held more tightly together.
Correct answer: stable