Unit 5 · Lesson 2d

2dNuclear Reactions and Fission/Fusion

Explore how splitting and combining nuclei release enormous energy via E = Δm·c², and how this powers reactors and stars.

Nuclear reactions power the Sun, generate electricity in nuclear plants, and explain the origin of elements. Understanding fission and fusion is essential for energy policy, astrophysics, and the future of clean energy.

Lesson Overview

Nuclear reactions release enormous energy by converting a tiny amount of mass into energy via Einstein's equation E = Δm·c². Fission splits heavy nuclei (like uranium) and powers nuclear reactors; fusion combines light nuclei (like hydrogen) and powers the Sun. Both processes release far more energy per reaction than any chemical process.

Key Concepts

Nuclear Fission

A heavy nucleus splits into two smaller nuclei + neutrons + energy

Chain Reaction

Neutrons from fission trigger further fissions; self-sustaining

Critical Mass

Minimum mass of fissile material needed to sustain a chain reaction

Nuclear Fusion

Two light nuclei combine to form a heavier nucleus + energy

Stellar Energy

Stars fuse hydrogen into helium, releasing energy for billions of years

Mass Defect Δm

Difference between reactant mass and product mass; converted to energy

Binding Energy

Energy = Δm × c²; energy released when nucleons bind together

Nuclear Power Plant

Uses controlled fission to heat water, drive turbines, generate electricity

Mass–Energy Equivalence

E = Δm · c²

Δm = mass defect (kg), c = speed of light = 3 × 10⁸ m/s, E = energy released (J).

1 atomic mass unit (u) = 1.66 × 10⁻²⁷ kg; 1 u of mass defect ≈ 931.5 MeV of energy.

Example 1

In a fission reaction, the mass defect is 3.20 × 10⁻²⁸ kg. How much energy is released?

Answer:E = Δm × c² = 3.20 × 10⁻²⁸ × (3 × 10⁸)² = 3.20 × 10⁻²⁸ × 9 × 10¹⁶ = 2.88 × 10⁻¹¹ J.
Example 2

Explain why a chain reaction requires a critical mass.

Answer:Each fission releases ~2–3 neutrons. If the sample is too small, most neutrons escape without hitting another nucleus and the reaction dies out. At critical mass, on average exactly one neutron per fission triggers another fission, sustaining the reaction.
Example 3

The Sun fuses 4 hydrogen nuclei (protons) into one helium-4 nucleus. The mass of 4 protons is 6.693 × 10⁻²⁷ kg; helium-4 mass is 6.645 × 10⁻²⁷ kg. Find the energy released per fusion.

Answer:Δm = 6.693 × 10⁻²⁷ − 6.645 × 10⁻²⁷ = 4.8 × 10⁻²⁹ kg. E = 4.8 × 10⁻²⁹ × (3 × 10⁸)² = 4.32 × 10⁻¹² J ≈ 27 MeV.
Example 4

Why does fusion require extremely high temperatures?

Answer:Fusion requires two positively charged nuclei to overcome their electrostatic repulsion (Coulomb barrier) and get close enough for the strong nuclear force to take over. Temperatures of ~10⁷ K give nuclei enough kinetic energy to do this.
Example 5

Compare the energy released per kilogram of fuel: fission vs. chemical combustion.

Answer:Fission of 1 kg of U-235 releases ~8 × 10¹³ J. Burning 1 kg of coal releases ~3 × 10⁷ J. Nuclear fission releases roughly 2–3 million times more energy per kilogram than chemical combustion.
Guided Problem 1

A fission reaction has a mass defect of 8.0 × 10⁻²⁹ kg. Calculate the energy released.

Hint: Use E = Δm × c² with c = 3 × 10⁸ m/s.

Guided Problem 2

Why is fusion harder to achieve on Earth than fission?

Hint: Think about the conditions needed to overcome electrostatic repulsion between nuclei.

Guided Problem 3

In a nuclear power plant, what is the role of the moderator (e.g., water)?

Hint: Neutrons need to be slowed down to be more effective at triggering fission.

Guided Problem 4

Which releases more energy per reaction: fission of U-235 or fusion of hydrogen? Explain.

Hint: Compare binding energy per nucleon for light vs. heavy nuclei.

Guided Problem 5

Why is nuclear waste from fission reactors a long-term problem?

Hint: Think about the half-lives of the fission products.

Key Vocabulary

Fission

The splitting of a heavy nucleus into two lighter nuclei, releasing energy and neutrons.

Example: U-235 + neutron → Ba-141 + Kr-92 + 3 neutrons + energy.

Fusion

The combining of two light nuclei into a heavier nucleus, releasing energy.

Example: The Sun fuses hydrogen into helium, releasing the energy that powers all life on Earth.

Mass Defect

The difference between the total mass of separate nucleons and the mass of the assembled nucleus.

Example: The mass defect of helium-4 is about 0.03 u, corresponding to ~28 MeV of binding energy.

Binding Energy

The energy equivalent of the mass defect; the energy needed to completely separate a nucleus into its nucleons.

Example: Iron-56 has the highest binding energy per nucleon — it is the most stable nucleus.

Interactive Practice — 5 Questions

1

What is the source of energy in nuclear fission?

2

A chain reaction becomes self-sustaining when:

3

Why does fusion require extremely high temperatures?

4

Which nucleus has the highest binding energy per nucleon?

5

In a nuclear power plant, the purpose of control rods is to:

Independent Practice

1

Describe the sequence of events in a nuclear fission chain reaction, from the initial neutron to sustained energy release.

2

A mass defect of 5.0 × 10⁻²⁸ kg is observed in a fusion reaction. Calculate the energy released in joules.

3

Compare nuclear fission and nuclear fusion: fuel used, products, energy released per reaction, and current technological status.

4

Explain why iron-56 is the most stable nucleus and how this relates to the energy released by fission and fusion.

5

★ Research the ITER fusion reactor project. Describe the fuel used, the confinement method, and why achieving net energy gain (Q > 1) is considered a milestone.

Challenge
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Common Mistakes

Thinking fission and fusion are the same process.

Fission splits heavy nuclei; fusion combines light nuclei. Both release energy, but by different mechanisms.

Assuming E = mc² means all mass is converted to energy in a nuclear reaction.

Only the mass defect Δm is converted to energy — the difference between reactant and product masses, which is a tiny fraction of the total mass.

Believing fusion is impossible on Earth.

Fusion has been achieved in hydrogen bombs and experimental reactors (like ITER); the challenge is achieving net energy gain in a controlled, sustained way.

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Math Tips

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Always use SI units in E = Δm·c²: mass in kg, c = 3 × 10⁸ m/s, energy in joules. To convert to MeV: 1 MeV = 1.6 × 10⁻¹³ J.