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Binding Energy Per Nucleon And Nuclear Stability

Key idea: Interpret the binding energy per nucleon curve, identify stable nuclei near iron, and relate the curve to energy release in fusion and fission (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Relate binding energy per nucleon to fission, fusion, applications and hazards.

1. Definitions (Must Know)

A. Binding energy per nucleon

The binding energy per nucleon is: E_b/A where E_b is the total binding energy and A is the nucleon number.

It is a useful measure of stability: larger E_b/A generally means nucleons are more tightly bound.

2. Key Ideas (What Earns Marks)

  • The curve of E_b/A vs A peaks around iron/nickel (A ≈ 56): these nuclei are among the most stable.
  • Light nuclei (A small) can release energy by fusion (moving up the curve).
  • Very heavy nuclei (A large) can release energy by fission (moving down towards the peak).

3. Detailed Explanations

Binding energy per nucleon curveBinding energy per nucleon rises steeply for light nuclei, reaches a broad maximum near iron and nickel, then decreases slowly for heavy nuclei. Arrows show fusion and fission moving toward the maximum.Nucleon number, ABinding energy per nucleonFe / Ni regionlightheavyfusionfissionproducts more tightly bound on average
Scroll diagram horizontally to read all labels.
Fusion of light nuclei and fission of very heavy nuclei can move products toward greater binding energy per nucleon. The increase in total binding energy is released.

A. How to read the curve

  • If a reaction moves nuclei to a higher E_b/A, the products are more tightly bound.
  • The difference in total binding energy appears as released energy (mainly kinetic energy and radiation).

B. Why fusion releases energy for light nuclei

For small A, the curve rises steeply. Combining two light nuclei to form a heavier nucleus closer to the peak increases E_b/A, so energy can be released.

C. Why fission releases energy for heavy nuclei

For very large A, splitting a heavy nucleus into two medium-mass nuclei moves the products closer to the peak (higher E_b/A), so energy can be released.

One-line linkage to fission/fusion

“Energy is released when the products have a higher binding energy per nucleon than the reactants.”

4. Common Mistakes

  • Saying “fusion always releases energy” (it releases energy mainly when light nuclei fuse towards the peak).
  • Confusing “binding energy per nucleon” with “binding energy” (total).
  • Reading the curve backwards (remember: higher E_b/A means more stable).

5. Exam Tips

  • If asked which process releases energy, compare where the nuclei sit on the E_b/A curve.
  • Use “move towards the peak near iron” as the key reasoning.
  • State what energy becomes: mainly kinetic energy of products and gamma radiation.

6. Worked Examples

Modelled example 1

Binding energy per nucleon calculation

Core

Problem

A nucleus has total binding energy E_b = 1.20 × 10⁻¹⁰ J and nucleon number A = 16. Find E_b/A.
Study the worked solution

  1. Normalise the total

    Method

    Divide the whole-nucleus binding energy by its nucleon number.

    Reason

    E_b/A is the average binding energy associated with each nucleon.

    Working

    E_b/A = (1.20 × 10⁻¹⁰)/16

  2. Evaluate

    Method

    E_b/A = 7.50 × 10⁻¹² J per nucleon.

    Reason

    The answer is an average energy, not the total binding energy.

    Working

    E_b/A = 7.50 × 10⁻¹² J nucleon⁻¹

Guided practice 2

Fusion vs fission reasoning

About 4 min

Problem

Explain why fusing two light nuclei can release energy, using the binding-energy-per-nucleon curve.

Try this before viewing the solution

Hints

Hint 1: track the vertical movement
Light-nucleus fusion moves the product toward the iron-region peak.
Hint 2: connect binding to release
State how higher E_b/A changes total binding and system mass-energy.
View solution step by step

  1. Read the light-nucleus region

    Method

    For small A, E_b/A rises steeply as nucleon number increases.

    Reason

    The fused product lies closer to the curve’s peak.

    Working

    light reactants → product with higher E_b/A

  2. Interpret the product

    Method

    The product’s nucleons are more tightly bound and its total binding energy is greater.

    Reason

    Higher binding energy per nucleon across the same conserved nucleon total means greater total binding.

    Working

    Δ E_b > 0

  3. State the energy outcome

    Method

    The increase in binding energy is released, mainly as kinetic energy and radiation.

    Reason

    The more tightly bound products have lower total mass-energy.

    Working

    lower product mass-energy → energy released

Common misconception 3

Which process releases energy? (given E_b/A)

Find and correct the mistake

Learner claim

Uranium-235 has E_b/A ≈ 7.6 MeV and its fission products average 8.5 MeV. A learner says the products “contain more energy,” so fission must absorb energy. Diagnose the claim.

Try this before viewing the solution

Energy outcome

View solution step by step

  1. Interpret higher binding

    Method

    The products are more tightly bound.

    Reason

    Their binding energy per nucleon is higher by about 0.9 MeV.

    Working

    8.5 > 7.6

  2. Correct the energy picture

    Method

    More tightly bound products have lower total mass-energy, not extra stored energy waiting to be supplied.

    Reason

    Binding energy is the energy required to separate the bound system.

    Working

    higher binding → lower bound-system mass-energy

  3. State the outcome

    Method

    Fission releases the mass-energy difference, mainly as fragment kinetic energy and radiation.

    Reason

    The products move toward the iron-region peak.

    Working

    reactants → more tightly bound products + released energy

Examiner practice 4

Energy release estimate from change in E_b/A

2 marks

Examination question

A heavy nucleus of A = 240 splits into products whose average binding energy per nucleon is higher by 0.9 MeV. Estimate the energy released in one fission event. [2 marks]

Try this before viewing the solution

View solution step by step

  1. Convert average increase to total

    1 mark

    Method

    Multiply the per-nucleon increase by the conserved nucleon total.

    Reason

    All 240 nucleons contribute to the change in total binding energy.

    Working

    Δ E ≈ A Δ(E_b/A)

  2. Evaluate

    1 mark

    Method

    Δ E ≈ 216 MeV.

    Reason

    The increase in total binding energy appears as released energy.

    Working

    Δ E ≈ 240(0.9) = 216 MeV

Challenge 5

Comparing stability (qualitative)

Minimal support

Independent transfer

Nucleus X has E_b/A = 8.7 MeV and nucleus Y has E_b/A = 7.9 MeV. Which is more stable by this measure, and what does that imply about separating its nucleons?

Try this before viewing the solution

Hints

Hint 1: interpret the larger average
Higher E_b/A means stronger average binding.
View solution step by step

  1. Compare the values

    Method

    Nucleus X is more stable by binding energy per nucleon.

    Reason

    8.7 MeV per nucleon exceeds 7.9 MeV per nucleon.

    Working

    8.7 > 7.9

  2. Interpret physically

    Method

    On average, more energy per nucleon must be supplied to separate X completely.

    Reason

    Its nucleons are more tightly bound.

    Working

    higher E_b/A → greater average separation energy

7. Mind Stretchers

Mind stretcher 1: Why are very heavy nuclei less stable?Extension

Show Answer

For very large A, E_b/A is lower than near the peak, meaning nucleons are (on average) less tightly bound. That makes heavy nuclei more likely to release energy by splitting into more stable mid-mass nuclei.

Mind stretcher 2: Why doesn’t E_b/A keep increasing forever?Extension

The strong nuclear force is attractive, so why does binding energy per nucleon stop increasing and start decreasing for very heavy nuclei?

Show Answer

The strong nuclear force is short-range: each nucleon strongly binds only to nearby nucleons, so the “extra binding” gained by adding more nucleons eventually saturates.

However, electric repulsion between protons is long-range and increases as more protons are added. For very heavy nuclei, increasing Coulomb repulsion reduces stability, so E_b/A decreases.

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Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027