Mass defect and binding energy
Key idea: A reviewed, static H2 Physics learning chain for all official Nuclear Physics outcomes, from Rutherford evidence to fusion and fission.
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The core idea
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Big question: Why does a bound nucleus have less mass than its separated nucleons?
Mass defect is the difference between the mass of separated nucleons and the nucleus. Its binding energy is Δmc²: the energy required to separate the nucleus completely. Binding energy per nucleon compares stability across nuclei and rises to a broad maximum near iron before slowly falling.
Calculate mass defect consistently
Mass defect is the mass of the separated protons and neutrons minus the mass of the bound nucleus. Binding energy is Δmc²: the energy needed to separate the nucleus completely, and the energy released when it forms.
Use either nuclear masses throughout or atomic masses in a way that cancels electron masses. Convert u to MeV/c² with 1 u c² = 931.5 MeV, or use SI masses consistently. A negative 'binding energy' usually means the subtraction was reversed.
Check your understanding: A nucleus has mass defect 0.020 u. Find its binding energy.
0.020(931.5) = 18.6 MeV.
Compare nuclei with binding energy per nucleon
Total binding energy generally grows with nucleon number, so stability comparisons use binding energy per nucleon. The curve rises steeply for light nuclei, reaches a broad maximum near iron/nickel and falls slowly for very heavy nuclei.
A larger value usually means nucleons are more tightly bound, but decay possibility also depends on the specific initial and final mass-energies and conservation laws. Read the curve as a trend, not an exact table of every reaction.
Check your understanding: Why not compare total binding energy alone?
Larger nuclei contain more nucleons and tend to have larger totals; energy per nucleon provides a meaningful average comparison.
Key ideas to keep
- Binding energy is positive even though a bound system has lower energy than separated parts.
- Use consistent atomic or nuclear masses so electron masses cancel correctly.
- Greater binding energy per nucleon generally means a more tightly bound nucleus.
See the reasoning
Worked example
Find total and per-nucleon binding energy
Question: Eight protons and eight neutrons total 16.1280 u; nucleus mass is 15.9905 u. Find mass defect and binding energy.
Step 1: Find the separated-nucleon mass
Why: The nucleus contains eight protons and eight neutrons.
Working: The stated separated total is 16.1280 u.
Step 2: Subtract the bound mass
Why: Mass defect is separated minus bound.
Working: Δm = 16.1280 − 15.9905 = 0.1375 u.
Step 3: Convert and average
Why: Total binding and binding per nucleon answer different questions.
Working: E = 0.1375(931.5) = 128 MeV; E/A = 128/16 = 8.0 MeV per nucleon.
Answer: Δm = 0.1375 u and E = Δmc² = 128 MeV, or 8.0 MeV per nucleon.
Check: The mass defect is positive because the bound system has lower rest mass.
Use a hint if needed
Practise with support
Try this
Mass defect doubles. State binding-energy factor.
Hint: Keep units consistent.
Check your answer
It doubles because E = Δmc².
Now work without the hint
Practise independently
Your turn
Define mass defect and binding energy, use E = mc² and describe the binding-energy-per-nucleon curve.
Check your answer
Mass defect is separated-nucleon mass minus nuclear mass. Its energy equivalent is the binding energy. Binding energy per nucleon rises rapidly for light nuclei, peaks near iron and declines slowly for heavy nuclei.
Avoid these traps
Common mistakes
Common mistake
Mass defect means matter vanishes.
What is wrong with this reasoning?
Show better thinking
The bound system's lower mass represents released binding energy.
Common mistake
Higher binding energy means a less stable nucleus.
What is wrong with this reasoning?
Show better thinking
Greater binding energy per nucleon generally means nucleons are more tightly bound.
Write for the examiner
Exam guidance
Write the mass-defect subtraction in words before inserting masses, then convert units only once.
Exam-style practice [5 marks]
A 12-nucleon nucleus has total binding energy 90 MeV. Find binding energy per nucleon and interpret it.
Plan before you answer
- Divide total binding by A.
- Give the correct unit.
- Interpret the average without treating nucleons independently.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
7.5 MeV per nucleon; it measures average energy needed per nucleon to separate the nucleus, not energy stored by each independent nucleon.
Come back in three days
Check what stayed with you
Recall question
Where is binding energy per nucleon greatest approximately?
Check the answer
Near medium-mass iron-region nuclei.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 20 excludes knowledge of positron emission in 20(g) and detailed knowledge of the antineutrino and particle zoo in 20(o). Nuclide equations conserve nucleon number, charge, mass-energy and momentum. Count data require background correction before population-law inference. Applications must relate half-life, penetration and ionisation to benefit and hazard. The binding-energy-per-nucleon curve, not a claim that mass disappears, explains fusion and fission energy release.
- GCE A-Level H2 PhysicsTopic 20(p) / Topic 20(q) / Topic 20(r) / Topic 20(s) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027