HomePhysicsP7: Radioactivity and ParticlesP7.6 Chain Reactions and Nuclear Reactors

P7: Radioactivity and Particles

P7.1 Atomic Structure and Nuclear CompositionP7.2 Radioactive Decay – Alpha, Beta, GammaP7.3 Half-life Applications and SafetyP7.4 Nuclear FissionP7.5 Nuclear FusionP7.6 Chain Reactions and Nuclear ReactorsP7.7 Nuclear Risks, Waste, and Safety
P7: Radioactivity and Particles

Chain Reactions and Nuclear Reactors

Controlling nuclear power for electricity generation

Nuclear reactor power plant

Chain Reactions and Nuclear Reactors

Controlling nuclear power for electricity generation

Chain Reaction Mechanism

A chain reaction occurs when neutrons released from one fission event trigger further fissions in neighboring uranium-235 nuclei. Each fission releases 2-3 neutrons, creating exponential growth: one fission leads to two, then four, then eight, doubling each generation in microseconds. When enough fissile material is present (critical mass), the reaction becomes self-sustaining.

Controlling Chain Reactions

Nuclear reactors use several mechanisms to control the chain reaction. Control rods made of boron or cadmium absorb excess neutrons—inserting them deeper reduces the reaction rate, while withdrawing them increases power. Moderators (water or graphite) slow fast neutrons to thermal speeds without absorbing them, since slow neutrons are more likely to cause U-235 fission than fast neutrons.

Nuclear Reactor Components

A typical reactor contains: fuel rods of enriched uranium (3-5% U-235); a moderator to slow neutrons; control rods to regulate the reaction; coolant (water or liquid sodium) to remove heat; a steel reactor vessel containing the core; and thick concrete biological shielding to prevent radiation escape.

Reactor Operation

Fission heat boils water into steam, which drives turbines connected to generators producing electricity. For steady operation, exactly one neutron per fission must cause another fission (critical state, k=1). If k<1, the reaction dies out (subcritical); if k>1, power increases (supercritical). Control rod position maintains the desired power level.

Nuclear Reactor Simulator
Explore chain reactions and reactor control mechanisms

Higher absorption = fewer neutrons cause fission

Generation
0
Neutrons
1
Multiplier (k)
1.67
Status
Supercritical
Neutron Population Graph
Gen 0Gen 0

Chain Reaction Tree (First 4 Generations)

1
Initial neutron hits U-235
2
2
2 neutrons released
4
4
4
4
4 neutrons released
8 neutrons...
Worked Example

A reactor is operating at critical state (k=1). The operator inserts the control rods 20% deeper. Explain the effect on the neutron population and power output.

Step 1: Understand the starting condition

At k=1 (critical), each generation has the same number of neutrons—steady state operation with constant power.

Step 2: Effect of inserting control rods

Deeper insertion means more boron/cadmium in the reactor core, which absorbs more neutrons.

Step 3: Impact on multiplication factor

Fewer neutrons survive to cause fission, so k decreases below 1 (subcritical).

Step 4: Result

With k<1, each generation has fewer neutrons than the previous. The neutron population decreases exponentially, and power output drops until a new equilibrium is reached or rods are withdrawn.

Answer: Inserting control rods 20% deeper increases neutron absorption, reducing k below 1 (subcritical). The neutron population decreases each generation, causing power output to fall.
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Chain Reaction

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QuizQuestion 1 of 10

In a chain reaction, how many neutrons are typically released per fission event?