Summary to follow. 4 syllabus statements · 14 questions · about twenty minutes.
Compiled from the IB Physics guide (first assessment 2025, updated November 2023) and our question bank ·
Specialist review in progress
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Assessed in Paper 1A (multiple choice), Paper 1B (data-based) and Paper 2 (short and extended response). IB Physics guide (first assessment 2025, updated November 2023).
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In preparation: 0 of 4 sections compiled and reviewed. The rest show key terms and common misconceptions from our question bank until they are.
Nuclear fission
Nuclear fission
The splitting of a heavy nucleus into two smaller nuclei of comparable mass (the fission fragments), usually with the release of two or three neutrons and energy. Nucleon number and charge are conserved. For uranium-235 about 200 MeV is released per fission, most of it as kinetic energy of the fragments.
Spontaneous fission
Fission of a nucleus without any particle being absorbed. Like radioactive decay it is random and spontaneous: each nucleus has a fixed probability per unit time of splitting, unaffected by temperature or pressure. It is a significant decay mode of some very heavy nuclides, such as californium-252, and a very rare one for uranium-238. Energy is released because the products have less rest mass than the parent.
Neutron-induced fission
Fission that follows the absorption of a neutron. When uranium-235 absorbs a slow (thermal) neutron it forms uranium-236 in an excited state, which splits, for example ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n. The neutron need bring almost no kinetic energy; the energy released comes from the decrease in total rest mass.
Energy released in fission (from masses)
The total rest mass of the products is less than that of the reactants. The energy released is E = Δmc², where Δm = (total mass of reactants) − (total mass of products), counting every neutron on each side. With masses in u, 1 u = 931.5 MeV c⁻² gives the energy in MeV; with masses in kg, E is in J. 1 MeV = 1.60 × 10⁻¹³ J.
Energy released in fission (from binding energies)
Energy released = (total binding energy of the products) − (total binding energy of the reactants). The total binding energy of a nucleus is its nucleon number A multiplied by its binding energy per nucleon; a free neutron has zero binding energy. A uranium nucleus (about 7.6 MeV per nucleon) splits into medium nuclei (about 8.5 MeV per nucleon), so the binding energy increases by roughly 0.9 MeV per nucleon, about 200 MeV per fission.
Students often think Any process in which a piece breaks off a heavy nucleus is fission, so α emission, in which a small fragment leaves the nucleus, is a kind of spontaneous fission. In fact No. In fission a heavy nucleus splits into two nuclei of comparable mass, usually with the release of neutrons. In α decay the nucleus emits a single small ⁴₂He nucleus and the daughter is only slightly lighter than the parent.
Students often think Nuclei split when the fuel is hot enough: fission is driven by temperature, the heat released by one fission makes further nuclei split, and the fission rate can be controlled by heating or cooling the fuel. In fact No. Spontaneous fission is random with a fixed probability per unit time, unaffected by temperature, and neutron-induced fission is caused by the absorption of a neutron. The thermal energy released in the fuel does not make further nuclei split; neutrons do.
Chain reaction
Chain reaction
A sequence of fissions in which neutrons released by one fission go on to cause further fissions. Each fission of uranium-235 releases two or three neutrons (about 2.4 on average), but some escape from the fuel and some are absorbed without causing fission. The reaction is self-sustaining when, on average, at least one neutron from each fission causes another fission.
Critical mass
The minimum mass of a fissile material in which a self-sustaining chain reaction can take place. In a smaller piece the surface area is large compared with the volume, so too many neutrons escape through the surface before they can cause fission. The critical mass depends on the shape and density of the material and on whether it is surrounded by a material that reflects neutrons back into it.
Subcritical, critical and supercritical
If on average fewer than one neutron from each fission causes a further fission, the number of fissions falls in each generation and the reaction dies away (subcritical). If exactly one does, the fission rate is steady (critical), as in a reactor running at constant power. If more than one does, the number of fissions is multiplied by the same factor in each generation and the rate grows rapidly (supercritical).
Students often think In a chain reaction every neutron released by a fission goes on to cause another fission, so any fission that releases more than one neutron makes the rate grow; neutrons lost from the fuel need not be considered. In fact No. Some neutrons escape from the fuel and some are absorbed without causing fission. The chain continues at a steady rate when, on average, exactly one neutron from each fission causes another fission.
Students often think The fragments produced by a fission split again, and this repeated splitting of smaller and smaller pieces is the chain reaction. In fact No. The fragments, such as barium-141 and krypton-92, are medium-mass nuclei that do not undergo fission; they decay by β⁻ emission. The chain is carried by the neutrons released in each fission.
Moderator
Moderator
Material in the core, such as water, heavy water or graphite, that slows the fast neutrons released in fission (kinetic energies of about 2 MeV) to thermal energies (about 0.025 eV at room temperature) through repeated elastic collisions with its nuclei. Slow neutrons are far more likely to be absorbed by uranium-235 and cause fission. A good moderator has light nuclei, so that a neutron gives up a large fraction of its kinetic energy in each collision, and absorbs few neutrons.
Control rods
Rods of a strong neutron absorber, such as boron or cadmium, that can be moved into or out of the core. Inserting them further absorbs more neutrons, so fewer are left to cause fission. They are adjusted so that on average exactly one neutron from each fission causes another fission, keeping the power steady, and are fully inserted to shut the reactor down.
Coolant and heat exchanger
The coolant (for example pressurized water or carbon dioxide gas) carries thermal energy from the core. In a heat exchanger the hot coolant flows through tubes and thermal energy is conducted through the tube walls to water in a separate secondary circuit, which boils; the steam drives the turbines. The two fluids do not mix, so the radioactive primary coolant stays inside the sealed primary circuit.
Shielding
Thick layers of steel and concrete (and, around spent fuel, water) that absorb the neutrons and γ radiation emitted from the core, so that people outside receive only a very small dose. α and β particles are absorbed within the fuel, its cladding and the reactor vessel and do not reach the shield.
Students often think Control rods are an on/off switch: whenever they are absorbing neutrons the chain reaction is dying away, so any absorption by the rods makes the fission rate decrease. In fact No. Control rods are positioned so that they absorb just enough neutrons for, on average, exactly one neutron from each fission to cause another fission. The reactor then runs at a steady rate with the rods partly inserted; inserting them fully shuts it down.
Students often think The moderator absorbs surplus neutrons, so the moderator and the control rods do the same job of keeping the chain reaction under control. In fact No. The moderator slows neutrons down by collisions and absorbs as few as possible. The control rods absorb neutrons to control the rate.
Fission products
Fission products
The nuclei formed in fission and their decay products. Heavy nuclei have a higher ratio of neutrons to protons than stable medium-mass nuclei, so fission fragments are neutron-rich and radioactive. They decay mainly by β⁻ emission, often with γ emission, in chains that end at a stable nuclide. Their half-lives range from fractions of a second (krypton-92, 1.8 s) to hundreds of thousands of years (technetium-99, 2.1 × 10⁵ years).
Decay heat
Thermal energy released by the radioactive decay of fission products and other nuclides in used fuel. It continues after the chain reaction has stopped, so spent fuel must be cooled, at first under water in pools, for years. It decreases with time as the short-lived products decay away.
Management and long-term storage of nuclear waste
Spent fuel is first stored under water, which removes decay heat and absorbs radiation, and later in shielded dry casks; high-level waste may be sealed in glass and metal containers for disposal deep in stable rock. Containment must keep radioactive nuclides out of groundwater and away from people until their activity has fallen far enough. Products such as caesium-137 and strontium-90 (half-lives about 30 years) dominate the activity for the first few centuries, but long-lived products such as technetium-99 (2.1 × 10⁵ years) require isolation for many thousands of years.
Students often think Radioactivity can be changed by temperature: heating or boiling a radioactive material destroys its radioactivity, and cooling it slows the decay and makes it safer. In fact No. The rate of radioactive decay is not affected by temperature, pressure or chemical change. Heating, boiling or cooling a sample leaves its half-life and activity unchanged.
Students often think Fission splits a large, unstable nucleus into smaller, stable nuclei, such as ordinary barium and krypton, so the products are not radioactive and can at most give out a little energy as γ rays. In fact No. Fission fragments are neutron-rich and radioactive, mostly β⁻ and γ emitters, with half-lives from fractions of a second to hundreds of thousands of years. They make spent fuel highly radioactive.
Diagnostic a bearings check, not a test
8 questions, one per part of the topic where we can. Answer them, then see which statements you own and which to read.
1 Some very heavy nuclides, such as californium-252, can undergo spontaneous fission, whereas uranium-235 in a reactor undergoes neutron-induced fission. Which statement about spontaneous fission is correct?
Answer and reasoning
Energy is released as kinetic energy of an α particle that breaks off the nucleus. — A student who counts any break-up of a nucleus as fission picks this. Californium-252 does emit α particles, but that is α decay, a separate process: it removes one small ⁴₂He nucleus, whereas in fission the nucleus splits into two fragments of comparable mass, such as barium and krypton.
Energy is released only once the material is hot enough for its nuclei to shake apart. — A student who thinks fission is driven by temperature picks this. Spontaneous fission is random, with a fixed probability per unit time for each nucleus, and heating the material does not change it; every fission releases energy, whatever the temperature.
No energy is released, as no neutron has been absorbed to supply the energy. — A student who thinks the absorbed neutron supplies the energy of fission picks this. The energy comes from the decrease in rest mass when the heavy nucleus becomes two medium-mass nuclei, so spontaneous fission releases energy too.
Energy is released when the nucleus splits into two fragments of comparable mass. — In spontaneous fission a heavy nucleus splits at random into two fragments of comparable mass without absorbing any particle. The products have less total rest mass than the parent, so energy is released, mostly as kinetic energy of the fragments, just as in neutron-induced fission.
2 A chain reaction of uranium-235 fission in a reactor core is proceeding at a steady rate. Which condition is being met?
Answer and reasoning
On average, exactly one of the neutrons from each fission causes a further fission. — Some neutrons escape and some are absorbed without causing fission. If on average exactly one neutron from each fission causes another fission, every generation has the same number of fissions and the rate is steady.
Each fission releases exactly one neutron, which goes on to cause a further fission. — A student who thinks every neutron released goes on to cause a fission reasons that a steady rate needs exactly one neutron per fission. A fission of uranium-235 releases two or three neutrons, about 2.4 on average; the rate is steady because, on average, all but one of them escape or are absorbed without causing fission.
The fission fragments split again in turn, each one releasing further neutrons. — A student who thinks the chain consists of fragments splitting again picks this. Fragments such as barium and krypton do not undergo fission; they decay by β⁻ emission. The chain is carried by the neutrons.
The moderator absorbs the surplus neutrons, leaving one per fission to continue the chain. — A student who reads 'moderate' as 'keep under control' picks this. A moderator slows neutrons and must absorb as few as possible; the surplus neutrons escape from the core or are absorbed without causing fission, for example by the control rods.
3 In a gas-cooled reactor, the uranium fuel rods sit in channels through a large block of graphite, which is the moderator. Carbon dioxide gas carries thermal energy from the core. What is the role of the graphite?
Answer and reasoning
It slows fast neutrons by collisions, as slow neutrons are more likely to cause fission. — Fission releases fast neutrons, with energies of about 2 MeV. Elastic collisions with the light carbon nuclei slow them to thermal energies, at which uranium-235 is far more likely to absorb them and undergo fission.
It absorbs surplus neutrons from the fuel, so that the rate of fission is kept under control. — A student who reads 'moderate' as 'keep under control' picks this. Absorbing neutrons to control the rate is the job of the control rods; a moderator must absorb as few neutrons as possible.
It speeds up the neutrons so that they hit uranium nuclei hard enough to split them. — A student who thinks fast neutrons split nuclei better, like bullets, picks this. Collisions with graphite nuclei can only slow neutrons; slow neutrons are the ones uranium-235 absorbs most readily.
It moderates the temperature of the core, stopping the fuel from overheating. — A student who takes 'moderator' to mean temperature control picks this. Here the carbon dioxide coolant carries thermal energy away; the graphite's role is to slow neutrons to thermal energies.
4 A fission of uranium-235 produces barium-141 (¹⁴¹₅₆Ba) and krypton-92 (⁹²₃₆Kr). The heaviest stable isotopes of these elements are barium-138 (¹³⁸₅₆Ba) and krypton-86 (⁸⁶₃₆Kr). Which decay are barium-141 and krypton-92 expected to undergo?
Answer and reasoning
β⁺ decay, which converts a surplus neutron into a proton — A student who has the two β decays the wrong way round picks this. In β⁺ decay a proton changes into a neutron, which would make the neutron excess worse; the neutron-to-proton change needs β⁻ decay.
α decay, which carries the surplus neutrons away — A student who thinks α decay removes excess neutrons picks this. An α particle removes two protons and two neutrons, which does not reduce the neutron excess of these fragments; they decay by β⁻ emission.
β⁻ decay, which turns a surplus neutron into a proton — Barium-141 has 85 neutrons against at most 82 in stable barium, and krypton-92 has 56 against at most 50. In β⁻ decay a neutron changes into a proton, reducing the neutron excess; both nuclides are β⁻ emitters.
γ decay only, as nuclei formed by fission are stable — A student who thinks fission products are ordinary stable nuclei picks this. Both fragments have more neutrons than any stable isotope of their element, so they are radioactive and decay by β⁻ emission.
Working Barium-141 has N = 141 − 56 = 85 neutrons; stable barium has at most 138 − 56 = 82. Krypton-92 has N = 92 − 36 = 56; stable krypton has at most 86 − 36 = 50. Both fragments have surplus neutrons, so they undergo β⁻ decay, in which a neutron changes into a proton (Z increases by 1, N decreases by 1).
5 In one neutron-induced fission of uranium-235, ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n. The atomic masses are 235.043928 u for uranium-235, 140.914403 u for barium-141 and 91.926173 u for krypton-92, and the mass of a neutron is 1.008665 u (the electron masses cancel). Take 1 u = 1.661 × 10⁻²⁷ kg = 931.5 MeV c⁻², 1 eV = 1.60 × 10⁻¹⁹ J and c = 3.00 × 10⁸ m s⁻¹. How much energy is released in this fission?
Answer and reasoning
3.3 × 10⁻¹⁰ J — A student who leaves the neutrons out of the mass balance uses 235.043928 − (140.914403 + 91.926173) = 2.203352 u, giving 3.3 × 10⁻¹⁰ J. The absorbed neutron and the three released neutrons all have mass; including them gives Δm = 0.186022 u.
2.8 × 10⁻¹¹ J — Including every neutron, the mass decreases by 236.052593 u − 235.866571 u = 0.186022 u = 3.090 × 10⁻²⁸ kg, so E = Δmc² = 3.090 × 10⁻²⁸ kg × 9.00 × 10¹⁶ m² s⁻² = 2.8 × 10⁻¹¹ J (173 MeV).
9.3 × 10⁻²⁰ J — A student who multiplies the mass by c instead of c² gets 3.090 × 10⁻²⁸ × 3.00 × 10⁸ = 9.3 × 10⁻²⁰. The unit of this product is kg m s⁻¹, not J; the energy equivalent needs c² = 9.00 × 10¹⁶ m² s⁻².
2.8 × 10⁻¹⁷ J — A student who finds 0.186022 × 931.5 = 173 MeV correctly but converts it with 1.60 × 10⁻¹⁹ J gets 2.8 × 10⁻¹⁷ J. That factor converts eV; 1 MeV = 1.60 × 10⁻¹³ J, so 173 MeV = 2.8 × 10⁻¹¹ J.
Working Mass of reactants = 235.043928 u + 1.008665 u = 236.052593 u. Mass of products = 140.914403 u + 91.926173 u + 3(1.008665 u) = 235.866571 u. Δm = 236.052593 u − 235.866571 u = 0.186022 u = 0.186022 × 1.661 × 10⁻²⁷ kg = 3.090 × 10⁻²⁸ kg. E = Δmc² = 3.090 × 10⁻²⁸ kg × (3.00 × 10⁸ m s⁻¹)² = 2.78 × 10⁻¹¹ J ≈ 2.8 × 10⁻¹¹ J. Check in MeV: 0.186022 u × 931.5 MeV u⁻¹ = 173.3 MeV = 173.3 × 1.60 × 10⁻¹³ J = 2.77 × 10⁻¹¹ J ≈ 2.8 × 10⁻¹¹ J.
6 In a reactor core, each fission of uranium-235 releases 2.5 neutrons on average. Of these, on average 0.7 escape from the core and 0.8 are absorbed by the control rods and other materials without causing fission. What happens to the rate of fission?
Answer and reasoning
It increases: each fission releases more neutrons than the one it absorbed. — A student who ignores lost neutrons sees 2.5 neutrons out for 1 in and expects growth. Only the neutrons that cause fission count: 2.5 − 0.7 − 0.8 = 1.0 per fission, so the rate stays constant.
It stays constant: on average one neutron per fission causes a fission. — Of the 2.5 neutrons, 0.7 + 0.8 = 1.5 do not cause fission, leaving 2.5 − 1.5 = 1.0 per fission that do. Each generation has the same number of fissions, so the rate is steady.
It decreases: control rods absorb neutrons and so shut the reaction down. — A student who thinks control rods only switch the reaction off picks this. The rods absorb 0.8 neutrons per fission, but 1.0 per fission still causes another fission, which holds the rate steady. At constant power the rods are always absorbing some neutrons.
It increases: the energy released heats the fuel, so that more nuclei split. — A student who thinks heat drives fission picks this. Nuclei are split by absorbing neutrons, not by the thermal energy of the fuel; with 1.0 neutron per fission causing fission, the rate stays constant.
Working Neutrons per fission that go on to cause a further fission = 2.5 − 0.7 − 0.8 = 1.0. Each generation therefore has the same number of fissions as the one before, so the rate of fission stays constant (the reactor is critical).
7 Pushing the control rods further into a reactor core reduces its power output. Why?
Answer and reasoning
They slow neutrons down, so the neutrons are less able to split nuclei. — A student who thinks faster neutrons are better at splitting nuclei picks this. Slowing neutrons is the moderator's job, and it makes fission of uranium-235 more likely, not less.
They absorb thermal energy, cooling the fuel so that fewer nuclei split. — A student who thinks the fission rate is set by the temperature of the fuel picks this. Thermal energy is removed by the coolant; the rods reduce the power by absorbing neutrons.
They absorb the fission fragments, which would otherwise split again. — A student who thinks the fragments continue the chain by splitting again picks this. The fragments stay in the fuel and do not undergo fission; the chain is carried by neutrons, which the rods absorb.
They absorb neutrons, so fewer neutrons are left to cause fission. — Control rods contain strong neutron absorbers such as boron or cadmium. Inserting them further removes more neutrons, so on average fewer than one neutron per fission causes another fission and the fission rate falls.
8 Spent fuel rods taken out of a reactor are stored for several years under a few metres of water in a pool. No chain reaction takes place in the pool, yet the pool water has to be cooled continuously. Why does the water need cooling?
Answer and reasoning
The rods still hold the thermal energy they gained in the core, which leaks out only slowly. — A student who pictures the rods as hot objects cooling down picks this. A rod merely cooling would lose its thermal energy to cold water within hours; cooling is needed for years because decay keeps releasing energy.
Keeping the rods cold slows down the decay of their fission products, making them safer. — A student who thinks temperature changes the rate of decay picks this. Radioactive decay is unaffected by temperature; the water is cooled to remove the decay heat, not to slow the decay.
Radiation from the rods makes the water radioactive, and the water's decay heats it. — A student who thinks exposure to radiation makes a material radioactive picks this. The γ radiation absorbed by the water deposits energy but does not make the water radioactive; the heating comes from decay in the rods.
The radioactive fission products keep decaying, and their decay energy heats the rods. — The spent fuel contains large amounts of radioactive fission products. Their decay continues after the chain reaction has stopped and releases thermal energy, decay heat, which the pool water must carry away for years.
Read the ones marked not yet in Learn, then Verify.
Verify confirm before you go
6 more questions. Every wrong answer here is a real misconception, and you see why it is wrong straight away.
1 In the fission ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2¹₀n, the binding energies per nucleon are 7.59 MeV for uranium-235, 8.29 MeV for xenon-140 and 8.59 MeV for strontium-94. A free neutron has no binding energy. Take 1 MeV = 1.60 × 10⁻¹³ J. How much energy is released in this fission?
Answer and reasoning
1.49 × 10⁻¹² J — A student who subtracts the binding energies per nucleon directly gets 8.29 + 8.59 − 7.59 = 9.29 MeV = 1.49 × 10⁻¹² J. Each value must first be multiplied by its nucleon number to give a total binding energy.
3.15 × 10⁻¹⁰ J — A student who takes the energy released to be the binding energy of the products gives 1968.06 MeV = 3.15 × 10⁻¹⁰ J. The uranium nucleus was already bound by 1783.65 MeV, so only the increase, 184.41 MeV, is released.
2.95 × 10⁻¹¹ J — The energy released is the increase in total binding energy: [140(8.29) + 94(8.59)] − 235(7.59) = 1968.06 − 1783.65 = 184.41 MeV, which is 184.41 × 1.60 × 10⁻¹³ J = 2.95 × 10⁻¹¹ J.
2.85 × 10⁻¹⁰ J — A student who thinks the binding energy of uranium is stored in it and released on splitting gives 235 × 7.59 = 1783.65 MeV = 2.85 × 10⁻¹⁰ J. That is the energy needed to separate uranium into free nucleons; fission releases only the gain in binding energy.
Working Total binding energy = A × (binding energy per nucleon). Reactants: ²³⁵U: 235 × 7.59 MeV = 1783.65 MeV; neutron 0. Products: ¹⁴⁰Xe: 140 × 8.29 MeV = 1160.60 MeV; ⁹⁴Sr: 94 × 8.59 MeV = 807.46 MeV; total 1968.06 MeV; neutrons 0. Energy released = 1968.06 MeV − 1783.65 MeV = 184.41 MeV = 184.41 × 1.60 × 10⁻¹³ J = 2.95 × 10⁻¹¹ J.
2 A sphere of pure uranium-235 has a mass slightly below the critical mass: a chain reaction started in it dies away. Which change, keeping the same mass of uranium-235, could allow it to sustain a chain reaction?
Answer and reasoning
Place a strong neutron source beside the sphere so more fissions start — A student who thinks the number of starting neutrons decides whether a chain continues picks this. The source starts more chains, but in each one fewer than one neutron per fission causes another fission, so every chain still dies away.
Heat the sphere strongly, so that its nuclei vibrate hard enough to split — A student who thinks fission is driven by temperature picks this. Nuclei are split by absorbing neutrons, not by thermal motion; heating makes the sphere expand, so its density falls and even more neutrons escape before causing fission.
Surround the sphere with a material that reflects escaping neutrons back into it — Below the critical mass too many neutrons escape through the surface. A reflector returns some of them to the uranium, so more neutrons per fission go on to cause fission; enough reflection raises this to one, and the chain becomes self-sustaining.
Cut the sphere into small pieces to expose more of its surface to neutrons — A student who applies the surface-area rule from chemical reaction rates picks this. Smaller pieces have more surface compared with volume, so even more neutrons escape before causing fission, and the chain dies away faster.
3 In a pressurized water reactor, water pumped through the core (the primary coolant) becomes radioactive, but the water turned into steam to drive the turbine does not. What makes this possible?
Answer and reasoning
The primary water mixes with cooler secondary water in the heat exchanger, which dilutes it until it is no longer radioactive. — A student who thinks a heat exchanger mixes the fluids, and that dilution removes radioactivity, picks this. The fluids are kept apart; mixing would spread the radioactive nuclides into the steam and the turbine, not remove them.
The circuits are separate: energy is conducted through heat-exchanger tube walls to water that does not enter the core. — In the heat exchanger the primary coolant flows inside sealed tubes and the secondary water flows around them. Thermal energy is conducted through the tube walls; no water crosses, and the secondary water is not exposed to the core's neutrons, so it stays non-radioactive.
Boiling the water into steam in the heat exchanger destroys the radioactivity the water picked up in the core. — A student who thinks heating changes radioactivity picks this. Radioactive decay is unaffected by temperature; the secondary water stays non-radioactive because it never mixes with the primary coolant.
The tube walls absorb the radiation from the primary water, which would otherwise make the water in the secondary circuit radioactive. — A student who thinks exposure to radiation makes things radioactive picks this. Absorbing γ radiation deposits energy in water but does not make it radioactive; what keeps the steam non-radioactive is that the two circuits never mix.
4 A reactor core is surrounded by thick layers of steel and concrete. What is the main purpose of these layers?
Answer and reasoning
To absorb the neutrons and γ radiation leaving the core, protecting people nearby — Neutrons and γ rays are penetrating and escape from the fuel and reactor vessel. Thick steel and concrete absorb them so that people outside the reactor receive only a very small dose. This is the shielding.
To stop α particles from the fuel, the most ionizing and most harmful radiation — A student who thinks the most ionizing radiation is the most dangerous everywhere picks this. α particles travel only a few centimetres in air and are stopped within the fuel itself; the shielding is there for neutrons and γ rays.
To contain the explosion if the chain reaction runs out of control, as in a bomb — A student who thinks a reactor can explode like a nuclear bomb picks this. Reactor fuel cannot produce a nuclear explosion; the shielding absorbs radiation during normal operation.
To keep thermal energy in the core, so that less is wasted to the surroundings — A student who treats the shielding as insulation picks this. Thermal energy is carried out of the core by the coolant to the heat exchanger; the layers are there to absorb radiation.
5 High-level waste from a reactor contains caesium-137, a fission product with a half-life of 30 years. The waste is kept in a store for 90 years. What percentage of the initial caesium-137 activity remains at the end of this time?
Answer and reasoning
12.5% — 90 years is 90 ÷ 30 = 3 half-lives. The activity halves three times: 100% → 50% → 25% → 12.5%.
33.3% — A student who divides by the number of half-lives gets 100% ÷ 3 = 33.3%. After n half-lives the activity has been halved n times, so it falls by a factor of 2³ = 8, not 3.
87.5% — A student who works out the fraction that has decayed, 1 − ⅛ = ⅞, gives 87.5%. That is the share of the caesium-137 nuclei that have decayed; the activity remaining is ⅛ of the initial activity, 12.5%.
6.25% — A student who lists the times 0, 30, 60 and 90 years and counts four half-lives gets (½)⁴ = 6.25%. Those four times mark only three intervals, so the activity halves three times.
Working Number of half-lives = 90 years ÷ 30 years = 3. Fraction of the activity remaining = (½)³ = ⅛ = 0.125, so 12.5% remains.
6 Spent fuel contains caesium-137 (half-life 30 years), strontium-90 (half-life 29 years) and technetium-99 (half-life 2.1 × 10⁵ years), produced in similar numbers by fission. Which conclusion about the long-term storage of this waste is correct?
Answer and reasoning
After about 60 years, two of their half-lives, the caesium-137 and strontium-90 in it have completely decayed. — A student who thinks the half-life is half the time to decay completely picks this. After two half-lives a quarter of the caesium-137 and strontium-90 nuclei remain; each half-life halves what is left, so they never decay completely, and the technetium-99 has hardly decayed at all.
Most of its activity at first comes from technetium-99, as it has by far the longest half-life of the three. — A student who thinks a long half-life means high activity picks this. In 30 years half of the caesium-137 nuclei decay but almost none of the technetium-99 nuclei do, so for similar numbers of nuclei far fewer technetium-99 nuclei decay each second, and at first its activity is far smaller.
Burying it deep in rock reduces its activity, since the rock absorbs the radiation that the waste emits. — A student who confuses absorbing radiation with reducing radioactivity picks this. Rock shields people from the radiation, but the number of nuclei decaying per second is unchanged; activity falls only as the nuclei decay.
It stays radioactive for far longer than 300 years, as the technetium-99 barely decays in that time. — In 300 years caesium-137 and strontium-90 pass through about 10 half-lives and fall to about 0.1% of their activity, but technetium-99 completes less than 0.2% of one half-life. Its activity persists for hundreds of thousands of years, so containment must last many thousands of years.
Working After 300 years (about 10 half-lives) the caesium-137 and strontium-90 activities have fallen to about (½)¹⁰ ≈ 1/1000 of their initial values. In 300 years technetium-99 completes only 300/(2.1 × 10⁵) ≈ 0.0014 of a half-life, so almost all of it remains. For similar numbers of nuclei, far fewer technetium-99 nuclei decay each second than caesium-137 nuclei, so its activity is much smaller at first, but it persists for hundreds of thousands of years.
That was your twenty minutes. Real practice on E.4 is past-paper questions marked against the mark scheme.
Paper 1A tests it as multiple choice; Paper 1B through data you have not seen before; Paper 2 with short answers and, at HL, extended responses. Look for the command words — outline, explain, compare, evaluate — and give exactly what each asks for.
Compiled from the IB Physics guide (first assessment 2025, updated November 2023) and our question bank · Specialist review in progress. How these pages are made · Free, no account ·
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