Sketch and interpret binding energy per nucleon
Describe the broad shape of binding energy per nucleon against nucleon number and use it to compare nuclear stability.
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. The Topic 23 outcomes were also checked against Cambridge’s 2028–2030 syllabus, which reports no significant teaching changes. Online practice is self-checked and cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use scientific notation, SI units, proportional reasoning and the particle numbers in nuclide notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What belongs on the horizontal axis for the binding-energy-per-nucleon curve?
What you will learn
- Sketch binding energy per nucleon against nucleon number
- Describe the rise for light nuclei, broad maximum around medium-mass nuclei and slow fall for heavy nuclei
- Compare average binding per nucleon from a supplied graph
Read the axes before describing the curve
Put nucleon number A on the horizontal axis and binding energy per nucleon on the vertical axis. The curve rises steeply for the lightest nuclei, reaches a broad maximum among medium-mass nuclei, then decreases gradually for the heaviest nuclei.
A sketch needs the overall trend and a labelled maximum region; it does not need invented point-by-point data. Read numerical values from a supplied graph only to its stated precision.
Greater binding per nucleon indicates tighter average binding
Binding energy per nucleon is the total nuclear binding energy divided by A. A larger value means more energy per nucleon would be needed, on average, to separate that nucleus into individual nucleons.
When a reaction moves products toward a higher binding energy per nucleon, the products are more tightly bound. Whether energy is released depends on the total binding energy of all reactants and products, not just the height of one point on the graph.
Pause and explain
Which curve shape is expected for binding energy per nucleon?
Worked example
A graph shows nuclei X and Y with binding energies per nucleon 7.2 MeV and 8.1 MeV. Which is more tightly bound on average?
Show the worked solution
- Read both values from the same vertical scale.
- Compare 8.1 MeV per nucleon with 7.2 MeV per nucleon.
- The greater value means more energy per nucleon is needed to separate the nucleus.
Answer Y is more tightly bound on average.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Sketch the expected binding-energy-per-nucleon curve from A = 1 to A = 240 and label both axes.
Give me a hint
Show the broad trend rather than trying to reproduce exact data.
Compare my reasoning
- Label the horizontal axis nucleon number A.
- Label the vertical axis binding energy per nucleon.
- Draw a steep initial rise, a broad maximum near medium mass, and a gradual decline toward heavy nuclei.
A rising curve to a broad medium-mass maximum followed by a slow fall.
Look for these in your work
- Correct axes
- Steep rise for light nuclei
- Maximum then gradual fall
A supplied graph gives 8.4 MeV per nucleon for nucleus P and 7.6 MeV per nucleon for Q. Compare their average binding.
Give me a hint
Use the same graph scale and compare the values per nucleon.
Compare my reasoning
- P has the larger plotted value: 8.4 MeV per nucleon.
- A higher value corresponds to more energy required per nucleon to separate the nucleus.
- Therefore P is more tightly bound on average.
P is more tightly bound per nucleon.
Look for these in your work
- Compares the per-nucleon values
- Interprets higher binding energy
- States the comparison
A student says that a product nucleus with greater binding energy per nucleon always means the reaction released energy. What extra comparison is required?
Give me a hint
Compare total binding energy for all reactants with total binding energy for all products.
Compare my reasoning
- A per-nucleon value is an average, not the total energy change.
- Find each nucleus’s total binding energy by combining its per-nucleon value with its nucleon number.
- Compare the total binding energies on the two sides.
Compare total binding energy of all products with total binding energy of all reactants.
Look for these in your work
- Recognises the per-nucleon average
- Uses nucleon number to find totals
- Compares both reaction sides
Common mistakes
- Putting nucleon number on the vertical axis
- Drawing a straight rising line that never turns over
- Claiming a reaction releases energy from one product’s binding-energy-per-nucleon value alone
What can you explain now?
What belongs on the horizontal axis for the binding-energy-per-nucleon curve?
Compare with the explanation
Nucleon number
The required variation is against nucleon number.
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Make it stick
What does a higher binding energy per nucleon tell you about average nuclear binding?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.