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Nuclear reactors and safety

In a thermal reactor a moderator slows the neutrons and control rods absorb the surplus, so that on average one neutron from each fission causes another. Moderators are made of light nuclei because a head-on elastic collision between equal masses transfers all the energy. Safe operation depends on being able to shut down, cool, shield and contain.

Nuclear reactors and safety: why cooling continues after shutdown

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Year 13AQA 3.8.1.7, 3.8.1.8 OCR A 6.4.4(h), 6.4.4(i)EDEXCEL 6, 8

Builds on Fission and fusion and Radioactive decay and the decay constant and Momentum and impulse.

IN THIS TOPIC

State the functions of the moderator, control rods and coolant, with example materials.
Give the factors behind each of those material choices.
Use the elastic collision model to explain why moderators are made of light nuclei.
Describe the safety features of a reactor, and the handling and storage of radioactive waste.

COMMON MISCONCEPTION

A nuclear reactor can explode like a nuclear bomb.

A reactor cannot explode like a bomb: its low-enriched fuel and control rods keep exactly one neutron per fission causing another fission; the worst failure is a meltdown, not a nuclear explosion.

The moderator, control rods and coolant

A thermal reactor holds the chain reaction steady: on average exactly one neutron from each fission goes on to cause the next. The moderator slows neutrons, control rods absorb excess neutrons to regulate the chain reaction, and the coolant transfers thermal energy from the core.

A labelled generic reactor core: cyan fuel rods stand in a moderator, amber control rods reach down between them to set the chain's pace, cool coolant enters low and leaves hot near the top on its way to the boilers, and the whole core sits inside thick concrete shielding. — FIG. 1A generic thermal reactor: fuel rods in a moderator, control rods between them, coolant in cool and out hot through thick shielding.

The moderator, filling the core around the fuel rods, slows the fast fission neutrons to thermal speeds so uranium-235 can capture them. The control rods absorb neutrons. Lower them further in and they thin the chain, so the power falls; withdraw them and it quickens. The coolant carries the thermal energy of the slowed fragments out of the core to boilers, where it raises steam for the turbines. No specific reactor design is examined, and this generic picture is all that is asked for.

Fuel for the common light-water designs is enriched to only a few per cent uranium-235, and some designs run on natural uranium with a graphite or heavy-water moderator; either way the fuel is far too dilute for the runaway growth a weapon needs, and the geometry and control systems hold the chain at one. A mismanaged reactor can overheat catastrophically, but it cannot undergo a nuclear detonation.

Why the moderator is light

The moderator's physics is a collision problem borrowed from mechanics. In a head-on elastic collision between a neutron of mass m and a stationary nucleus of mass M, the neutron keeps a fraction of its kinetic energy,

\text{fraction kept} = (\frac{M - m}{M + m})^{2}

NOT IN THE AQA DATA BOOKLET: LEARN IT

Moderating a neutron: light atoms take the energy (animated figure) — FIG. 2Why a moderator is made of light atoms: in a head-on elastic collision a neutron stops dead on hydrogen, handing over everything; bounces off carbon-12 still keeping nearly three quarters of its energy; and rebounds off uranium-238 with almost everything it arrived with.

Equal masses swap completely. Strike a proton head-on and the neutron stops dead, like one snooker ball on another. Against carbon-12 it keeps 72%, and against uranium-238 over 98%. An effective moderator is therefore made of light nuclei, and it must also absorb few neutrons and stay cheap and stable inside a reactor core. Water and graphite are the standard examples. Control rods want the opposite virtue, strong neutron absorption, so boron and cadmium take that job. Coolants must carry heat well without absorbing neutrons or corroding, and water again, or carbon dioxide, does it.

The safety case

Fresh fuel is only mildly radioactive; almost everything else in the safety case follows from what fission makes. The neutron-rich fragments are intensely active β⁻ and γ emitters, so spent fuel is handled remotely, by machinery behind barriers, from the moment it leaves the core. The core itself sits inside metres of concrete and steel shielding that attenuate the neutrons and gamma rays of a working reactor down to controlled levels outside.

For emergency shut-down, the control rods drop fully into the core, absorbing enough neutrons to stop the chain reaction outright. Around all of it sits a sealed containment structure, the last barrier, whose job is to hold radioactive material in if the inner ones are breached.

Spent fuel activity against time on a logarithmic scale: two dashed straight component lines, one steep and short-lived, one shallow and long-lived, with the cyan total bending from the first onto the second, the early years spent in cooling ponds and the long tail in sealed deep storage. — FIG. 3Spent fuel activity on a log scale: the short-lived fragments rule the early years, the long-lived tail sets the storage time.

Waste is half-life arithmetic. Spent rods typically spend some years in cooling ponds on site, where water shields the radiation and carries away the heat while the short-lived fragments burn themselves out. How long depends on the design and the country's rules. What remains is dominated by long-lived isotopes, so it is sealed, often in glass, and destined for secure deep storage lasting many thousands of years. Storage time is set by the half-lives of the longest-lived components, exactly the logic of the decay lesson.

GUIDED PRACTICE

Shut down, still hot

A reactor is shut down by driving its control rods fully in. Explain, through the neutron budget, why the chain reaction stops, and why the fuel nonetheless continues to produce heat for a long time afterwards.

Show the working

Fully inserted rods absorb so many neutrons that fewer than one per fission survives to cause another. The multiplication factor, meaning the average number of fissions each fission goes on to cause, falls below one, and the chain reaction stops within moments.

But the fuel is now crowded with neutron-rich fission fragments, and their radioactive decay carries on to its own half-lives, indifferent to any control rod. Decay heat is the reason cooling must continue long after shutdown, and the reason loss of cooling is the accident that dominates the safety case.

Risk, benefit and the decision

The course ends by asking for judgement. On one side, a reactor delivers vast, reliable, low-carbon energy out of very little fuel. On the other, rare accidents with severe consequences, and waste that must be stewarded for generations. Physics does not make the decision, but it quantifies both sides in doses, half-lives and joules. A question here asks you to weigh one named benefit against one named risk, and the answer should take that form.

ASSESSMENT FOCUS

State each of the three functions as an action. The moderator slows neutrons to thermal speeds, the control rods absorb neutrons to set the rate, and the coolant transfers energy out of the core. Moderator and control rods have opposite jobs, so swapping them describes a reactor that cannot work.
Material choices come with reasons attached. A moderator is light and barely absorbing, so water or graphite. Control rods absorb strongly, so boron or cadmium. A coolant shifts heat well and absorbs little, so water again, or carbon dioxide.
The elastic collision model fits in one line. Equal masses transfer all the kinetic energy head-on, so light nuclei slow neutrons in few collisions while heavy ones barely slow them at all.
Emergency shut-down means the control rods drop fully into the core. Say fully, and say absorb. Waste answers then follow a chain of their own. Fission fragments are neutron-rich beta and gamma emitters, so handling is remote, cooling ponds cover the short-lived years, and sealed deep storage takes the long-lived tail.

CHECK YOURSELF

In a head-on elastic collision with a stationary nucleus of mass M, a neutron of mass m keeps the fraction ((M − m)/(M + m))² of its kinetic energy. Compare a collision with hydrogen (M = m) and with carbon-12 (M = 12m), and hence explain why water moderates in fewer collisions than graphite.

Show a hint

Substitute the two masses; then think about what the fractions mean per bounce.

Show the answer

For hydrogen, (0/2m)² = 0, so a head-on strike hands over every joule in a single collision.

For carbon-12, (11m/13m)² = 121/169 = 0.72, so the neutron keeps 72% and loses barely more than a quarter per head-on bounce.

Real collisions are rarely head-on, so several are always needed, but hydrogen-rich water still thermalises neutrons in far fewer collisions than graphite, because the lighter the target nucleus, the greater the fraction of energy transferred in each collision.

The moderator slows neutrons, control rods absorb excess neutrons to regulate the chain reaction, and the coolant transfers thermal energy from the core.

Reactor fuel is far too dilute to detonate; overheating is the real danger.

Four layers of safety: shut it down, cool it, shield it, contain it.

WORKBOOK

Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.

18 questions on this topicAnswer them one at a time and mark yourself against the mark scheme.Practise this topic

Or read them with their mark schemes on the nuclear reactors and safety questions page.

8 flashcards on this topicDefinitions, off-sheet equations and a spot-the-error card, scheduled by spaced repetition in your browser.Revise with flashcards

WHERE TO GO NEXT

Exponentials and logarithms is the maths this lesson leans on, worked through step by step.

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State the functions of the moderator, control rods and coolant, with example materials.
Give the factors behind each of those material choices.
Use the elastic collision model to explain why moderators are made of light nuclei.
Describe the safety features of a reactor, and the handling and storage of radioactive waste.

Open the full revision checklist to track your progress across the whole unit.