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Nuclear Fission

Key idea: Explain nuclear fission and why it releases energy using the binding energy per nucleon curve; write nuclear equations and common exam explanations (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. Nuclear fission

Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei (plus other particles, often neutrons).

B. Why energy can be released

Fission can release energy because the products often have a higher binding energy per nucleon than the original heavy nucleus.

2. Key Ideas (What Earns Marks)

  • Explain energy release using the binding energy per nucleon curve: heavy nuclei sit lower than mid-mass nuclei, so splitting moves products towards higher E_b/A.
  • Nuclear equations must conserve:
    • nucleon number A
    • charge/proton number Z
  • Fission commonly releases neutrons, which can trigger further fissions (chain reaction idea).
One-line explanation

“Energy is released because the fission products have a higher binding energy per nucleon than the parent nucleus.”

3. Detailed Explanations

A. Typical fission equation (example)

One commonly quoted example (one of several possible channels) is: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n

Checks:

  • A: 235 + 1 = 236, and 141 + 92 + 3 = 236
  • Z: 92 + 0 = 92, and 56 + 36 = 92

Very heavy nuclei have lower E_b/A than nuclei near iron. If fission products lie closer to the peak, total binding energy increases, so energy is released as kinetic energy of fragments and radiation.

4. Common Mistakes

  • Forgetting to balance A and Z separately.
  • Saying fission “creates energy” (it releases energy due to a mass defect; mass–energy is conserved).
  • Confusing fission with fusion.

5. Exam Tips

  • Use the binding-energy-per-nucleon argument (it is the cleanest explanation).
  • Mention where the energy goes: mainly kinetic energy of fragments + neutrons + gamma.
  • If “chain reaction” is mentioned, define it briefly: neutrons from one fission can trigger more fissions.

6. Worked Examples

Modelled example 1

Balancing a fission equation

Core

Problem

Complete ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + x ¹₀n.
Study the worked solution

  1. Check charge

    Method

    Total Z is already balanced at 92.

    Reason

    Neutrons have zero charge, so this check cannot determine x.

    Working

    92 + 0 = 56 + 36

  2. Conserve nucleon number

    Method

    The left side has 236 nucleons and the named fragments account for 233.

    Reason

    Every emitted neutron adds one to the right-side nucleon total.

    Working

    235 + 1 = 236, while 141 + 92 = 233

  3. Find multiplicity

    Method

    x = 3 neutrons.

    Reason

    Three additional nucleons make the totals equal.

    Working

    233 + x = 236 ⇒ x = 3

Guided practice 2

Explaining energy release

About 4 min

Problem

Explain concisely why fission of a very heavy nucleus can release energy.

Try this before viewing the solution

Hints

Hint 1: locate products on the curve
Compare the parent and medium-mass products’ binding energies per nucleon.
Hint 2: state the energy destination
Connect increased total binding to lower product mass-energy and released kinetic energy or radiation.
View solution step by step

  1. Compare average binding

    Method

    Medium-mass fission products generally have higher E_b/A than the very heavy parent.

    Reason

    The products lie closer to the iron-region peak.

    Working

    heavy parent → products higher on E_b/A curve

  2. Compare total mass-energy

    Method

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

    Reason

    The increase in total binding energy corresponds to a mass decrease.

    Working

    greater binding → lower product mass

  3. State the release

    Method

    The difference appears mainly as fragment and neutron kinetic energy and gamma radiation.

    Reason

    Mass–energy is conserved; energy is released, not created.

    Working

    Δ E = Δ mc²

Common misconception 3

Balancing a plutonium fission equation

Find and correct the mistake

Learner claim

For ²³⁹₉₄Pu + ¹₀n → ¹⁴⁴₅₆Ba + ⁹⁴₃₈Sr + x ¹₀n, a learner says x = 0 because charge already balances. Diagnose the incomplete check and find x.

Try this before viewing the solution

Unit: neutrons

View solution step by step

  1. Confirm but limit charge balance

    Method

    Z balances: 94 = 56 + 38.

    Reason

    This only shows no charged particle is missing; neutrons do not affect Z.

    Working

    94 + 0 = 56 + 38

  2. Check nucleon number

    Method

    The left has 240 nucleons, while the two named fragments have 238.

    Reason

    The incident neutron contributes one to the initial total.

    Working

    239 + 1 = 240, while 144 + 94 = 238

  3. Find missing neutrons

    Method

    x = 2.

    Reason

    Two neutrons supply the two missing nucleons without changing charge.

    Working

    238 + x = 240 ⇒ x = 2

Examiner practice 4

Fissions needed for a given energy output

3 marks

Examination question

A reactor releases 1.0 × 10⁹ J in a short interval. If each fission releases about 200 MeV, estimate the number of fissions. Take 1 MeV = 1.60 × 10⁻¹³ J. [3 marks]

Try this before viewing the solution

View solution step by step

  1. Convert one-fission energy

    1 mark

    Method

    E_f = 3.2 × 10⁻¹¹ J.

    Reason

    Convert the per-event energy to the same unit as the total.

    Working

    E_f = 200(1.60 × 10⁻¹³) = 3.2 × 10⁻¹¹ J

  2. Form the event count

    1 mark

    Method

    N = E/E_f.

    Reason

    The total is the per-fission energy multiplied by the number of fissions.

    Working

    N = (1.0 × 10⁹)/(3.2 × 10⁻¹¹)

  3. Evaluate

    1 mark

    Method

    N = 3.1 × 10¹⁹ fissions.

    Reason

    The enormous count reflects the microscopic energy per event.

    Working

    N = 3.1 × 10¹⁹

Challenge 5

Neutron multiplication (simple chain model)

Minimal support

Independent transfer

Each fission releases three neutrons on average, but in a simplified reactor model only two neutrons per fission trigger another fission; the rest escape or are absorbed. How many new fissions occur in the next generation after 10 initial fissions?

Try this before viewing the solution

Unit: fissions

Hints

Hint 1: use the effective multiplier
Each initial fission produces two successful triggers for the next generation.
View solution step by step

  1. Identify the effective factor

    Method

    The next-generation multiplication factor in this model is two.

    Reason

    Only two of the three emitted neutrons cause further fission.

    Working

    k_effective = 2 new fissions per fission

  2. Apply one generation

    Method

    There are 20 new fissions.

    Reason

    Multiply the ten initial fissions by the effective factor.

    Working

    Nₙₑₓₜ = 2(10) = 20

7. Mind Stretchers

Mind stretcher 1: Why are slow (thermal) neutrons often effective at inducing fission?Extension

Show Answer

For some fissile nuclei, absorbing a neutron makes the nucleus unstable and more likely to split. A slow neutron is more likely to be captured (larger capture probability) than a fast neutron, increasing the chance of inducing fission.

Mind stretcher 2: Why are control rods needed?Extension

In a nuclear reactor, why are control rods (neutron absorbers) essential for steady operation?

Show Answer

Fission is a chain reaction: neutrons from one fission can trigger further fissions.

Control rods absorb excess neutrons to keep the reaction at a steady rate (preventing runaway increase in power) while still allowing enough neutrons to sustain the chain reaction.

8. Optional (Enrichment)

A. Videos (optional)

Continue with the next resource in this course.

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