Worked example 1
Balance this fission event: n + ²³⁵U → ¹⁴¹Ba + ⁹²Kr + ? neutrons
Try it first: Add the mass numbers on each side and see what is missing.
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Fission and FusionCourse level: High School / HonorsCourse level: AP Chemistry
Nuclear Fission and Fusion
What you'll be able to do: Distinguish fission from fusion, explain why each releases energy, and describe how a chain reaction is controlled in a reactor.
Best after: Types of Nuclear Decay and Balancing Nuclear Equations
Introduction
Fission splits a heavy nucleus and fusion joins light ones, yet both release enormous energy. The reason is the same in each case, and it is worth getting straight before the numbers appear.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Define nuclear fission and nuclear fusion and give an example of each
- Explain why selected heavy-nucleus fission and light-nucleus fusion reactions release energy using mass and binding energy
- Describe a chain reaction, critical mass, moderators and control rods
- Explain how high temperatures and quantum tunneling help positively charged nuclei undergo fusion
- Compare the fuel, conditions and products of fission and fusion
Fission: splitting a heavy nucleus
A slow neutron is absorbed by a ²³⁵U nucleus, which becomes unstable and splits into two mid-sized fragments plus two or three fresh neutrons and a large amount of energy, on the order of 200 MeV per event.
The fragments are not fixed; fission produces a distribution of products.
¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy
Chain reactions and critical mass
Because each fission releases more neutrons than it consumes, the reaction can sustain itself. That only happens if enough of those neutrons hit other fissile nuclei rather than escaping the sample, which is why a minimum critical mass is required. Below it the reaction fizzles out.
Criticality concerns the effective multiplication factor keff: below one the neutron population falls, at one it stays steady on average, and above one it grows. Critical mass is therefore not one universal number belonging only to an element; composition, shape, neutron leakage and surrounding materials affect whether a configuration sustains a chain. A moderator mainly slows neutrons by scattering, whereas control absorbers remove neutrons. Some reactor designs operate with fast neutrons and do not use the same moderation scheme.
Thermal-neutron U-235 fission illustrates one reactor fuel cycle; criticality and fuel requirements depend on the reactor design.
Inside a reactor
The moderator, often water or graphite, slows fast neutrons to thermal speeds so ²³⁵U absorbs them efficiently. Control rods made of neutron absorbers such as boron or cadmium are lowered into the core to soak up surplus neutrons and hold the reaction exactly self-sustaining.
Raising them speeds the reaction up; lowering them shuts it down.
Fusion joins selected light nuclei
Fusion combines light nuclei through reactions whose energetics depend on the specific isotopes and products. A useful example is ²H + ³H → ⁴He + n, releasing about 17.6 MeV. In stars, the net conversion of four protons to helium occurs through several steps and includes positrons and neutrinos; four protons do not simply collide simultaneously.
The positive nuclei repel electrically. High temperature supplies a high-energy tail, and quantum tunneling helps them reach separations where the strong nuclear interaction matters. High temperature alone is insufficient for useful fusion: sufficient density and confinement time are also needed. D–T fusion produces energetic neutrons that can activate surrounding materials; claiming that fusion creates no radioactive waste is inaccurate. Its waste characteristics differ from fission, but depend on fuel and reactor materials.
4 ¹₁H → ⁴₂He + 2 ⁰₊₁e + energy
Compare binding energies for the specified reaction
An energy-releasing nuclear reaction has products with lower total mass-energy than its reactants. Increased total binding energy provides the released energy after accounting for all particles. The average binding-energy-per-nucleon curve rises toward the iron/nickel region and then declines, explaining why selected light-nucleus fusion and heavy-nucleus fission can release energy. It does not prove that every possible fusion below iron or every split above iron is exothermic. Specific isotope masses settle a proposed reaction.
| Feature | Typical induced U-235 fission | D–T fusion example |
|---|---|---|
| Reacting nuclei | Heavy U nucleus plus neutron | Deuterium and tritium |
| Initial challenge | Sustain suitable neutron population | Bring repelling nuclei close enough |
| Products | Distribution of fragments and neutrons | He-4 and a neutron |
| Energy comparison | About 200 MeV per fission event | About 17.6 MeV per D–T event |
| Material consequences | Radioactive fission fragments and activation | Tritium handling and neutron activation |
Per-event energy and energy per fuel mass are different comparisons: a heavy fission nucleus contains many more nucleons than a D–T pair.
The broad binding-energy maximum is near iron/nickel. Check specific isotope masses before claiming a fusion or fission reaction releases energy.
Criticality is about effective neutrons
A fission event may release several neutrons, but not every neutron causes another fission: some escape or are absorbed without sustaining the chain.
| Effective-neutron condition | Chain behavior |
|---|---|
| Critical operation means | that on average one effective neutron from each fission triggers the next fission, keeping the rate steady. |
| More than one effective neutron | causes a growing chain; |
| fewer than one | causes it to die out. |
Scroll horizontally if needed to read all columns.
Count successful follow-on fissions, not just emitted neutrons.
Key ideas
Definition
Fission
Splitting a heavy nucleus into two mid-sized nuclei plus neutrons and energy.
Definition
Fusion
Combining nuclei into a heavier nucleus; selected light-isotope fusion reactions release energy when product mass-energy is lower.
Definition
Critical mass
A critical amount for a specified material and configuration; composition, geometry, surroundings and neutron losses affect it.
Rule
Moderator vs control rod
A moderator slows neutrons down; a control rod absorbs them.
Key concept
Common cause
Both processes release energy because the products have a higher binding energy per nucleon than the reactants.
Equation
Representative fission
¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n
- n = neutron, which both starts and continues the chain
Equation
Solar fusion (net)
4 ¹₁H → ⁴₂He + 2 ⁰₊₁e + 2 neutrinos + released energy
- e(+1) = positron
Equation
Mass-energy equivalence
E = mc²
- m = mass converted to energy
- c = speed of light
Worked examples
Worked example 2
Why can D–T fusion and U-235 fission both release energy despite changing nuclear size in opposite directions?
0 of 3 steps revealed.
Worked example 3
A fission releases three neutrons, but two escape or are absorbed without causing fission. Classify the chain condition if the third triggers one new fission.
Try it first: Find the average number of successful next fissions.
0 of 3 steps revealed.
Common mistakes
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Mixing up the moderator and the control rods. | They do opposite jobs: the moderator slows neutrons so they are more likely to cause fission, while control rods remove neutrons from the core. | Remember moderator = moderate the speed; control rod = control the number. |
| Saying fusion is easy because the nuclei are small. | Both nuclei are positively charged and repel each other strongly at short range, so enormous kinetic energy is needed. | Tie the temperature requirement to electrostatic repulsion, not to nuclear size. |
| Claiming any nucleus splitting releases energy. | The broad binding-energy trend favors heavy-nucleus fission, but a specific proposed split must be checked from reactant and product masses. | Check which side of the binding energy peak the reactant sits on. |
Scroll horizontally if needed to read all columns.
After the lesson · Question bank
Independent practice
Work through new problems on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
15 topic questions across 2 difficulty levels.
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What you should now know
Fission splits a heavy nucleus into fragments and neutrons, while fusion combines selected light nuclei. In an energy-releasing example the products have lower total mass-energy and greater binding overall. Fission-chain behavior depends on effective successor fissions, neutron leakage and absorption; moderators and control absorbers have distinct roles. Fusion needs suitable nuclei, high-temperature conditions and confinement, and neutron-producing fusion can activate surrounding materials.
- Fission splits a heavy nucleus; fusion joins light nuclei
- Fission of ²³⁵U releases 2-3 neutrons, allowing a chain reaction above the critical mass
- Moderators slow neutrons; control rods absorb them
- Fusion needs millions of kelvin to overcome repulsion between positive nuclei
- Both release energy because the products are more tightly bound per nucleon
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