Nuclear Binding Energy and Mass Defect
Mass Defect and Binding Energy
Mass defect
A bound nucleus has less mass than the total mass of its free constituent nucleons. The missing mass is the mass defect , and it corresponds to the binding energy through .
Interpretation
A larger binding energy generally means a more stable nucleus, but stability also depends on neutron-to-proton ratio and decay channels.
How to calculate binding energy
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Step 1: Find the masses of free protons and free neutrons.
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Step 2: Subtract the actual nuclear mass from the total free-nucleon mass to get .
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Step 3: Multiply by to obtain .
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Step 4: Optionally divide by to get binding energy per nucleon .
Common stability indicators
| Quantity | Meaning |
|---|---|
| Average binding per nucleon | |
| Mass excess | Deviation from integer mass units |
| Separation energy | Energy needed to remove a nucleon |
| Q-value | Net energy released or absorbed |
What does a positive binding energy indicate?
Positive binding energy means work must be supplied to separate the nucleus into free nucleons.
Correct answer: Energy is required to separate nucleons
Write the equation relating binding energy to mass defect.
Mass-energy equivalence connects the missing mass to the energy needed to bind the nucleus.
Correct answer: B = Δm c^2
Binding Energy per Nucleon
Trend across the chart of nuclides
The binding energy per nucleon rises rapidly for light nuclei, reaches a broad maximum near iron and nickel, and then slowly decreases for very heavy nuclei. This pattern explains why both fusion of light nuclei and fission of heavy nuclei can release energy.
Why can both fusion and fission release energy?
Energy is released when products are more tightly bound, moving toward the peak in near iron.
Correct answer: Because increases toward iron from both sides
Around which region of the periodic table does binding energy per nucleon peak?
The maximum is broadly around the iron-group nuclei.
Correct answer: near iron and nickel