L-27: Nuclear Fission and Fusion
Physics — Class 12 · NIOS Code 312 · Module 7 · Source: 312_Physics_Eng_Lesson27.pdf
Nuclear Fission and Fusion
Nuclear fission releases enormous energy in reactors and weapons; nuclear fusion powers stars and promises clean future energy. This lesson compares chemical and nuclear reactions, explains fission/fusion mechanisms, reactor design, and peaceful applications. Module 7: Atoms and Nuclei.
27.1 Chemical and Nuclear Reactions
27.1.1 Chemical Reactions
Valence electrons rearrange; nucleus unaffected. Energy ~eV (e.g. C + O₂ → CO₂ + 4.08 eV). Mass change ~10⁻³⁵ kg — practically conserved. Atom count of each element balanced on both sides.
27.1.2 Nuclear Reactions
Nuclei interact → new elements (transmutation). Energy ~MeV. Coulomb barrier (~3 MeV for C, ~20 MeV for Pb) must be overcome by projectile. Neutrons are ideal projectiles — no Coulomb repulsion; even thermal neutrons (0.0253 eV) can induce reactions.
Rutherford (1919): ⁴He + ¹⁴N → ¹⁷O + ¹H + 6.5 MeV (endothermic overall needs 1.2 MeV supplied). Exothermic example: ²⁷Al + ⁴He → ³⁰Si + ¹H + 10.7 MeV (~700,000× energy per event vs burning one C atom).
27.1.3 Conservation Laws
- Sum of mass numbers A conserved
- Sum of atomic numbers Z conserved
- Total energy (including mass-energy) conserved
- Momentum conserved — kinetic energy shared among products
27.2 Nuclear Fission
Discovery (1938): Hahn & Strassmann — slow neutrons on uranium produced barium (not transuranics) + ~200 MeV. Meitner & Frisch explained via liquid-drop model; named "fission."
Mass defect Δm ≈ 0.215 u → ~200 MeV
Average 2.54 neutrons per fission · event in ~10⁻¹⁷ s
Liquid-drop model (Bohr & Wheeler): neutron capture adds ~6.8 MeV/nucleon excitation; nucleus oscillates spherical ↔ dumbbell; Coulomb repulsion between fragments overcomes surface tension → split. ²³⁵U more fissile than ²³⁸U.
27.2.2 Nuclear Chain Reaction
Each fission releases 2–3 neutrons → can trigger more fissions. Self-sustained: neutron production rate = loss rate.
- Controlled chain reaction: nuclear reactor (control rods absorb excess neutrons)
- Uncontrolled chain reaction: atom bomb (Hiroshima, Aug 6 1945 — ~20,000 ton TNT equivalent)
One fission event releases ~7×10⁵ times energy of burning one carbon atom.
27.3 Nuclear Reactor
First reactor: Fermi, Chicago (1942). Components:
- Core: fuel rods (²³⁵U), moderator (slows neutrons in thermal reactors), control rods (Cd/B — absorb neutrons)
- Coolant: removes fission heat (heavy water or ordinary water)
- Reflector: reduces neutron leakage
- Pressure vessel, shielding (concrete), airtight reactor building
Heat → steam → turbine → electricity. Research reactors discharge heat to sea/river.
27.4 Nuclear Fusion
Two light nuclei combine → heavier nucleus + energy. From BE/A curve: fusion of H→He releases more energy per nucleon than fission.
Requires ~10 million K (Sun centre ~20 million K)
Overcome Coulomb repulsion between positive nuclei
Sun consumes ~400×10⁶ ton hydrogen per second
1 g deuterium → ~100,000 kWh · ocean deuterium nearly inexhaustible
Fusion harder to achieve on Earth than fission (extreme temperature + confinement). Controlled thermonuclear fusion is active research area. Hydrogen bomb uses uncontrolled fusion.
27.5 Nuclear Energy
India (Bhabha's 3-stage plan): (1) PHWR with natural uranium → electricity + Pu; (2) fast breeder reactors → breed U-233 from thorium; (3) thorium-based surplus fissile material. Reactors: Tarapur, Kota, Kaiga, Narora, Kalpakkam, Kakrapar.
27.5.2 Hazards and RBE
Radiation causes ionisation, cancer, genetic damage, sterility. RBE (relative biological effectiveness): γ/X/β = 1; thermal neutrons = 2–5; fast neutrons = 10; α = 10–20. Safety: avoid nuclear tests, careful waste disposal (salt mines), minimal medical radiation doses.
FISSION & FUSION — KEY POINTS
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Chemical reaction : ~eV ; nucleus unchanged
Nuclear reaction : ~MeV ; transmutation
Conservation : A, Z, energy, momentum
Fission : ²³⁵U + n → fragments + 2–3n + 200 MeV
Chain reaction : controlled = reactor ; uncontrolled = bomb
Reactor parts : fuel, moderator, control rods, coolant, shield
Fusion : light nuclei → heavier ; needs ~10⁷ K
Sun : 4¹H → ⁴He + 26.8 MeV
India reactors : PHWR (pressurised heavy water)
Quick Revision
- Neutrons best for inducing nuclear reactions — no Coulomb barrier.
- ²³⁸U becomes β-active after neutron capture (high n/p ratio).
- Fissile materials have odd mass number, even atomic number.
- Fusion releases more energy per unit mass than fission (~6.7 vs ~0.84 MeV/u).
- Spent reactor fuel is highly radioactive; wastes stored in sealed salt mines.
Q1. In a chemical reaction, the energy involved is typically of the order of:
Q2. The best projectile for inducing nuclear reactions is:
Q3. Nuclear fission of ²³⁵U releases approximately:
Q4. A substance that undergoes fission by thermal neutrons is called:
Q5. In a controlled nuclear chain reaction, excess neutrons are absorbed by:
Q6. The moderator in a thermal reactor is used to:
Q7. Nuclear fusion requires temperature of approximately:
Q8. The energy source of the Sun is:
Q9. India primarily uses which type of reactor for power generation?
Q10. Which radiation has the highest RBE (relative biological effectiveness)?
PYQ — Previous Year Questions
Extracted from NIOS Physics (312) board exam papers in your PDF. Chapter L27 — Nuclear Fission and Fusion only. Use Model Answer for marking points; Explanation for concept clarity.
Chapter 27 — Nuclear Fission and Fusion (L27)
3 questions · Sections A & B · Sources: 312/MAY/204A–C, 68/ESS/1-312-A
Section A — Objective (1 mark)
PYQ1. Read the passage: “In nuclear reactions, the nuclei of the reactants interact with each other and result in the formation of new elements… nuclear reactions can be endothermic or exothermic.” (b) Which of the following energy values of neutron can cause fission chain reaction in ²³⁵₉₂U? (A) Less than 0·1 eV (B) Greater than 1·0 eV (C) Greater than 7·7 MeV (D) Less than 7·0 eV but greater than 1·0 eV
Model Answer
(A) Less than 0·1 eV
Thermal (slow) neutrons (~0.025 eV at room temperature) efficiently induce fission in ²³⁵U and sustain a controlled chain reaction in a reactor.
Explanation
²³⁵U is fissile by thermal neutrons; fast neutrons are less likely to cause fission capture. Moderator in reactors slows neutrons to this energy range (L27 §27.2).
Section A — Short Answer (2 marks)
PYQ2. Fill in the blanks: (i) ___________ is a device in which a sustained, nuclear chain reaction is carried out in a controlled manner. (ii) The enormous energy produced by the sun is generated as a result of __________ reaction.
Model Answer
(i) Nuclear reactor — controlled chain reaction (control rods absorb excess neutrons)
(ii) nuclear fusion — Sun fuses hydrogen into helium at ~10⁷ K core temperature
Explanation
Reactor = peaceful controlled fission; Sun’s power = thermonuclear fusion, not fission (L27 §27.2–§27.3).
Section B — Short Answer (2 marks)
PYQ3. What is nuclear fusion? Write an equation of nuclear fusion to support your answer.
Model Answer
Nuclear fusion is the process in which two nuclei of lighter elements (such as hydrogen) fuse to form a heavier nucleus (such as helium), and a neutron may be emitted; a large amount of energy is released.
Example: ²₁H + ²₁H → ³₂He + ¹₀n + energy
(Sun: 4¹H → ⁴He + 2e⁺ + 2ν + 26.8 MeV also acceptable as fusion equation.)
Explanation
Fusion releases more energy per nucleon than fission but needs ~10⁷ K to overcome Coulomb repulsion between positive nuclei (L27 §27.3).
Problem Solving — L27 Nuclear Fission and Fusion
Six problems spanning this chapter’s NIOS syllabus. Every question is built from the notes and formula sheet: solve with equations first, then read the formal textbook-style write-up, the easy explanation, and the topic in depth (formulas, meaning, exam tips). Explanations open by default.
Define nuclear fission and name one fissile isotope used in reactors.
Solution — step by step with formulas
- Heavy nucleus splits into medium-mass fragments with energy release.
- e.g. ²³⁵U.
Final answer: ²³⁵U fission example
Textbook formal language
Fission liberates energy because BE/nucleon is higher for medium mass products.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Big nucleus cracks into mid-size pieces that are more tightly bound—energy spills out.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Nuclear fission
Neutrons emitted can sustain a chain reaction.
Link to chapter notes (L27 — Nuclear fission): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Distinguish controlled and uncontrolled chain reactions.
Solution — step by step with formulas
- Controlled: reactor, neutron population steady (moderator/control rods).
- Uncontrolled: explosion, rapid multiplication.
Final answer: Reactor vs bomb: neutron economy control
Textbook formal language
Multiplication factor k ≈ 1 critical; k>1 supercritical.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
If each fission’s neutrons cause one more fission, steady power; if more than one, runaway.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Chain reaction
Control rods absorb neutrons (Cd, B).
Link to chapter notes (L27 — Chain reaction): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Define fusion and state why high temperature is required.
Solution — step by step with formulas
- Light nuclei combine to heavier; need high KE to overcome Coulomb barrier.
Final answer: High T for Coulomb barrier penetration
Textbook formal language
Fusion of light nuclei increases BE/nucleon up to Fe region.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Nuclei repel; must smash together very fast (hot plasma) to stick.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Nuclear fusion
Powers stars; hydrogen isotopes fuse in stages.
Link to chapter notes (L27 — Nuclear fusion): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Why does fission of ²³⁵U release energy in terms of binding energy per nucleon?
Solution — step by step with formulas
- Products have higher BE per nucleon than ²³⁵U ⇒ total mass decreases ⇒ energy released.
Final answer: Higher BE/A of fragments ⇒ energy out
Formulas used in this problem
Textbook formal language
Mass defect of reaction appears as KE of fragments and neutrons plus radiation.
Working formula set for this problem: Q = Δm c². In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Pieces are ‘more glued’ than original—leftover mass becomes energy.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Energy release
Typical ~200 MeV per ²³⁵U fission.
Link to chapter notes (L27 — Energy release): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: Q = Δm c². In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write Q = Δm c² before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Why are moderators used in thermal reactors?
Solution — step by step with formulas
- Slow fast fission neutrons to thermal energies where fission cross-section of ²³⁵U is high.
Final answer: Slow neutrons for efficient ²³⁵U fission
Textbook formal language
Elastic scattering on light nuclei reduces neutron energy without much absorption ideally.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Fast neutrons zoom past fuel; slowed (water/graphite) they are more easily captured for fission.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Moderator role
H₂O, D₂O, graphite common moderators.
Link to chapter notes (L27 — Moderator role): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Give one advantage of fusion over fission for power (in principle).
Solution — step by step with formulas
- Abundant fuel (isotopes of H), less long-lived radioactive waste (in ideal scenarios).
Final answer: Cleaner fuel cycle / abundant fuel (principle)
Textbook formal language
Engineering confinement (magnetic/inertial) remains challenging on Earth.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Fusion aims for star-like power with lighter radioactive burden, but hard to contain.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Comparison
Both release energy via BE curve.
Link to chapter notes (L27 — Comparison): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).