IB Physics E.4 Fission — Notes (SL & HL)
Written by Evan Kotronis for the IB Diploma Physics course (first assessment 2025). E.4 has no additional higher level content: everything on this page is examinable at both SL and HL. The one purple HL box is an optional link back to HL material in E.3. The page builds on mass defect and binding energy (E.3) and on energy, power and efficiency (A.3).
What this page covers
- Why energy is released when a heavy nucleus splits, both spontaneously and after absorbing a neutron
- Calculating the energy released in a fission reaction from masses or from binding energies
- What a chain reaction is, and how it is kept under control (critical, subcritical and supercritical)
- The job of the moderator, control rods, heat exchanger and shielding in a nuclear power station
- The properties of fission products and how spent fuel and nuclear waste are managed, including the impact of long-term storage
In one minute
- Fission is the splitting of a heavy nucleus into two smaller nuclei of similar mass, plus a few neutrons. It can be spontaneous or neutron-induced (e.g. uranium-235 absorbing a slow neutron).
- The products have a greater binding energy per nucleon than the original nucleus, so the total mass decreases and energy \(E=\Delta m\,c^2\) is released — about 200 MeV per fission, mostly as kinetic energy of the fragments.
- Each fission releases 2–3 neutrons that can cause further fissions: a chain reaction. A reactor keeps exactly one neutron per fission going on to cause another fission.
- Moderator: slows neutrons down. Control rods: absorb neutrons. Heat exchanger: transfers thermal energy from the reactor coolant to water that becomes steam. Shielding: absorbs neutrons and γ radiation.
- Fission products are neutron-rich, highly radioactive and hot; some have very long half-lives, so spent fuel is cooled under water and then stored in sealed containers, eventually deep underground.
Why does splitting a heavy nucleus release energy?
- Binding energy per nucleon is about 7.6 MeV for uranium-235 but about 8.3–8.6 MeV for the medium-mass nuclei it splits into (E.3). Every nucleon ends up more tightly bound.
- More tightly bound means less mass: the products have less rest mass than the reactants. The mass decrease \(\Delta m\) appears as energy \(E=\Delta m\,c^2\).
- Only a small fraction of the mass is converted — under 0.1 % — but per kilogram of fuel this is millions of times more energy than any chemical reaction.
E.4 Binding energy curve simulation: pick a heavy nucleus and a pair of fission products, and see how the gain in binding energy per nucleon becomes the energy released.
Spontaneous and neutron-induced fission
| Spontaneous fission | Neutron-induced fission | |
|---|---|---|
| What triggers it | nothing: the nucleus splits on its own, at random, like any radioactive decay | the nucleus absorbs a neutron and becomes a highly unstable compound nucleus, which splits almost at once |
| Examples | californium-252 (about 3 % of its decays; used as a neutron source to start reactors); uranium-238 very rarely — roughly one decay in two million is fission, the rest are α decays | uranium-235 (and plutonium-239) absorbing a slow (thermal) neutron: \({}^{235}\text{U}+{}^{1}\text{n}\rightarrow{}^{236}\text{U}\rightarrow\) fragments + neutrons |
| Can the rate be controlled? | no — set by the nuclide, unaffected by temperature or pressure | yes — by controlling the number of neutrons available |
| Use | source of the first neutrons; background neutron emission from heavy nuclides | energy production in nuclear power stations |
In every fission reaction nucleon number and proton number are conserved. Uranium-235 does not always split the same way: many different pairs of fragments are possible, with mass numbers mostly around 90–100 and 135–145, so equations with different products are all correct as long as they balance.
\[ {}^{235}_{\;92}\text{U}+{}^{1}_{0}\text{n}\;\rightarrow\;{}^{141}_{\;56}\text{Ba}+{}^{92}_{36}\text{Kr}+3\,{}^{1}_{0}\text{n} \] \[ {}^{235}_{\;92}\text{U}+{}^{1}_{0}\text{n}\;\rightarrow\;{}^{140}_{\;54}\text{Xe}+{}^{94}_{38}\text{Sr}+2\,{}^{1}_{0}\text{n} \]In one neutron-induced fission of uranium-235, the products are xenon-140, an isotope of strontium and two neutrons: \({}^{235}_{\;92}\text{U}+{}^{1}_{0}\text{n}\rightarrow{}^{140}_{\;54}\text{Xe}+{}^{A}_{Z}\text{Sr}+2\,{}^{1}_{0}\text{n}\).
(a) Deduce \(Z\) and \(A\) for the strontium nucleus. (b) The stable isotope of strontium with the most neutrons is strontium-88. Compare the number of neutrons in the two strontium nuclei and state what this suggests about the fission product.
(a) Proton number: \(92+0=54+Z+0\Rightarrow\) Z = 38
Nucleon number: \(235+1=140+A+2\times1\Rightarrow\) A = 94
(b) Strontium-94 has \(94-38=56\) neutrons; strontium-88 has \(88-38=50\). The fission product has 6 more neutrons than the heaviest stable isotope: it is neutron-rich, so it is radioactive and will decay by β− emission (section 7).
How do you calculate the energy released in fission?
There are two equivalent routes. Use whichever matches the data you are given.
Route 1 — from masses
\[ \Delta m=m_{\text{before}}-m_{\text{after}} \] \[ E=\Delta m\,c^2 \]- \(m_{\text{before}}\), \(m_{\text{after}}\) = total mass of all particles before and after; \(\Delta m\) = mass decrease (kg, or u), \(c=3.00\times10^{8}\ \text{m s}^{-1}\), \(E\) = energy released (J). \(E=mc^2\) is in the data booklet; the expression for \(\Delta m\) is not.
- Working in u: multiply \(\Delta m\) by 931.5 MeV (data booklet: 1 u = 931.5 MeV c−2). Convert to joules with 1 MeV = 1.60 × 10−13 J.
- Include every particle: the incoming neutron on the left and all emitted neutrons on the right (\(m_n=1.008665\ \text{u}\)).
- Atomic or nuclear masses? Either works if you are consistent. With atomic masses the electrons cancel, because the proton numbers balance (92 = 56 + 36): 92 electrons on each side.
Route 2 — from binding energies
\[ E=\textstyle\sum \text{BE}_{\text{products}}-\sum\text{BE}_{\text{reactants}} \] \[ \text{BE}=A\times(\text{BE per nucleon}) \]- BE = binding energy (MeV), \(A\) = nucleon number. Free neutrons have zero binding energy, so they do not appear in the sum.
- Multiply each binding energy per nucleon by its own nucleon number first, then subtract. Not in the data booklet — it follows from the definition of binding energy.
For the reaction \({}^{235}_{\;92}\text{U}+{}^{1}_{0}\text{n}\rightarrow{}^{141}_{\;56}\text{Ba}+{}^{92}_{36}\text{Kr}+3\,{}^{1}_{0}\text{n}\), the atomic masses are: uranium-235, 235.043928 u; barium-141, 140.914411 u; krypton-92, 91.926156 u. Mass of a neutron = 1.008665 u.
(a) Calculate the energy released, in MeV and in J. (b) Calculate the percentage of the initial mass that is converted to energy.
(a) Mass before \(=235.043928+1.008665=236.052593\ \text{u}\)
Mass after \(=140.914411+91.926156+3\times1.008665=235.866562\ \text{u}\)
\(\Delta m=236.052593-235.866562=0.186031\ \text{u}\)
\(E=0.186031\times931.5=\) 173 MeV (173.3 MeV)
\(E=173.3\times1.60\times10^{-13}=\) 2.77 × 10−11 J
(b) \(\dfrac{0.186031}{236.052593}\times100=\) 0.079 %
Going via kilograms, \(\Delta m=0.186031\times1.661\times10^{-27}=3.09\times10^{-28}\ \text{kg}\) and \(E=\Delta m\,c^2=2.78\times10^{-11}\ \text{J}\). The tiny difference comes from rounding in the data-booklet constants; both answers are accepted.
Binding energies per nucleon: uranium-235, 7.591 MeV; xenon-140, 8.291 MeV; strontium-94, 8.594 MeV. Refer to the energy-level diagram above.
(a) Show that the energy released in \({}^{235}\text{U}+{}^{1}\text{n}\rightarrow{}^{140}\text{Xe}+{}^{94}\text{Sr}+2\,{}^{1}\text{n}\) is about 180 MeV. (b) Explain why the neutrons are left out of the calculation. (c) Explain why the answer differs from worked example 2.
(a) Total binding energies: U-235: \(235\times7.591=1783.9\ \text{MeV}\); Xe-140: \(140\times8.291=1160.7\ \text{MeV}\); Sr-94: \(94\times8.594=807.8\ \text{MeV}\).
Products: \(1160.7+807.8=1968.6\ \text{MeV}\)
\(E=1968.6-1783.9=\) 185 MeV (184.7 MeV) ≈ 180 MeV
(b) A free neutron is not bound to anything, so its binding energy is zero; the neutrons add nothing to either side.
(c) The fragments are different. Xe-140 + Sr-94 have a larger total binding energy than Ba-141 + Kr-92 + one extra free neutron, so this split releases more energy. Every fission of U-235 releases roughly, but not exactly, 200 MeV.
What is a chain reaction, and how is it controlled?
- Each fission of U-235 releases on average about 2.5 neutrons. Some escape from the fuel; some are absorbed by other nuclei without causing fission; some cause new fissions.
- If on average more than one neutron per fission causes another fission, the number of fissions per second rises exponentially (supercritical) — the principle of a nuclear weapon.
- If exactly one does, the rate is constant (critical) — the normal running state of a reactor.
- If fewer than one does, the reaction dies away (subcritical) — the state of a shut-down reactor.
- Critical mass: the minimum mass of fissile fuel in which a chain reaction can be sustained. In a small piece of fuel too many neutrons escape through the surface before they can cause fission; a larger mass has less surface area per unit volume, so fewer neutrons are lost.
The number of neutrons in one generation divided by the number in the previous generation is sometimes called the multiplication factor \(k\) (a useful idea, not a required term). After \(n\) generations the number of neutrons is \(N_0k^n\).
E.4 Fission chain reaction simulation: fire a neutron into a block of uranium-235, change the amount of fuel and insert control rods, and watch the reaction die away, stay steady or run away.
What do the main parts of a nuclear power station do?
A thermal-neutron power station turns the kinetic energy of fission fragments into thermal energy in the fuel, carries that energy away in a coolant, uses it to make steam, and drives a turbine and generator — exactly like a fossil-fuel power station from the steam onwards.
| Part | What it is made of | Role |
|---|---|---|
| Fuel rods | uranium oxide, enriched from the natural 0.7 % to about 3–5 % uranium-235 | contain the fissile nuclei; the kinetic energy of the fragments heats the rods |
| Moderator | water, heavy water or graphite — nuclei of low mass that absorb few neutrons | slows down the fast neutrons released by fission (about 2 MeV) to thermal energies (about 0.025 eV), at which they are far more likely to cause fission of U-235 |
| Control rods | boron or cadmium — good neutron absorbers | inserted further to absorb more neutrons and reduce the fission rate; withdrawn to increase it; fully inserted to shut the reactor down |
| Coolant | water (or a gas such as CO2) | carries thermal energy away from the core; keeps the fuel at a safe temperature |
| Heat exchanger (steam generator) | tubes carrying hot coolant through water in a separate circuit | transfers thermal energy from the primary coolant to the secondary water, which boils to make steam; the radioactive coolant never reaches the turbine |
| Shielding | thick steel pressure vessel and concrete walls (several metres), plus the water | absorbs neutrons and γ radiation from the core so that workers and the public receive a negligible dose |
How does the fission rate set the power output?
Every fission releases a definite energy (about 200 MeV for U-235). The thermal power of the reactor is therefore fixed by how many fissions happen each second:
\[ P_{\text{thermal}}=\frac{\text{fissions}}{\text{second}}\times\frac{\text{energy}}{\text{fission}} \] \[ \eta=\frac{\text{useful power out}}{\text{total power in}} \]- \(P\) in W; energy per fission in J (convert from MeV). The power relation is not in the data booklet; the efficiency \(\eta\) is (A.3).
- Like any thermal power station, a nuclear station can convert only about a third of the thermal energy into electrical energy. Most of the rest is transferred to the cooling water at the condenser.
A reactor core produces thermal power at a rate of 3.00 GW. Each fission of uranium-235 releases 200 MeV. The overall efficiency of the station is 34 %, as shown in the Sankey diagram. Mass of a U-235 atom = 235 u.
(a) Calculate the number of fissions per second. (b) Determine the mass of uranium-235 used up in one day. (c) Determine the electrical power output and the power transferred to the surroundings. (d) Coal releases 30 MJ kg−1 when burned. Estimate the mass of coal that would give the same thermal energy in one day.
(a) \(200\ \text{MeV}=200\times1.60\times10^{-13}=3.20\times10^{-11}\ \text{J}\)
Rate \(=\dfrac{3.00\times10^{9}}{3.20\times10^{-11}}=\) 9.4 × 1019 s−1 (9.375 × 1019 s−1)
(b) Fissions per day \(=9.375\times10^{19}\times86\,400=8.10\times10^{24}\)
Mass \(=8.10\times10^{24}\times235\times1.661\times10^{-27}=\) 3.16 kg per day
(c) \(P_{\text{el}}=0.34\times3.00=\) 1.02 GW; power to the surroundings \(=3.00-1.02=\) 1.98 GW
(d) Thermal energy per day \(=3.00\times10^{9}\times86\,400=2.59\times10^{14}\ \text{J}\); coal \(=\dfrac{2.59\times10^{14}}{30\times10^{6}}=\) 8.6 × 106 kg (about 8600 tonnes) — some 2.7 million times the mass of U-235.
How does the moderator slow neutrons down?
A fast neutron collides with moderator nuclei, giving some of its kinetic energy to the nucleus in each collision (momentum and, ideally, kinetic energy are conserved, A.2). The closer the mass of the moderator nucleus to the neutron's mass, the more energy is transferred per collision — which is why light nuclei are used. After many collisions the neutron is in thermal equilibrium with the moderator.
In a graphite-moderated reactor, a neutron of speed \(v\) collides head-on with a stationary carbon-12 nucleus. Take the mass of the carbon nucleus to be 12 times the mass \(m\) of the neutron. After the collision the neutron moves back along its original line with speed \(\tfrac{11}{13}v\).
(a) Determine the speed of the carbon nucleus after the collision. (b) Show that the collision is elastic. (c) Show that the neutron keeps about 72 % of its kinetic energy. (d) Estimate the minimum number of such collisions needed to slow a 2.0 MeV neutron to 0.025 eV. (e) Explain why hydrogen nuclei (in water) slow neutrons in fewer collisions.
(a) Take the neutron's initial direction as positive. Momentum: \(mv=m\left(-\tfrac{11}{13}v\right)+12mV\)
\(12V=v+\tfrac{11}{13}v=\tfrac{24}{13}v\Rightarrow\) V = 2v/13 ≈ 0.154v, in the neutron's original direction.
(b) Kinetic energy after, as a fraction of \(\tfrac12mv^2\): \(\left(\tfrac{11}{13}\right)^2+12\left(\tfrac{2}{13}\right)^2=\tfrac{121}{169}+\tfrac{48}{169}=1\). Total kinetic energy is unchanged, so the collision is elastic.
(c) Fraction kept \(=\left(\tfrac{11}{13}\right)^2=\tfrac{121}{169}=\) 0.716 ≈ 72 %
(d) After \(n\) collisions \(E=E_0(0.716)^n\). Need \(\dfrac{E_0}{E}=\dfrac{2.0\times10^{6}}{0.025}=8.0\times10^{7}\).
\(n=\dfrac{\ln(8.0\times10^{7})}{\ln(1/0.716)}=54.5\Rightarrow\) at least 55 collisions
(e) A hydrogen nucleus (proton) has almost the same mass as a neutron, so in a head-on collision it can take almost all of the neutron's kinetic energy. Much more energy is transferred per collision, so fewer collisions are needed.
Real collisions are mostly glancing, not head-on, so a neutron needs more than 55 collisions in graphite. The answer to (d) is a minimum.
What are the properties of fission products, and how is nuclear waste managed?
- Neutron-rich. Heavy nuclei need proportionally more neutrons than medium nuclei to be stable. When U-235 splits, the fragments inherit this high proportion of neutrons, so each decays by a series of β− decays (a neutron becomes a proton) towards a stable nuclide, e.g. Kr-92 → Rb-92 → Sr-92 → Y-92 → Zr-92 (stable) and Ba-141 → La-141 → Ce-141 → Pr-141 (stable).
- Highly radioactive. Many fragments have short half-lives, so freshly removed (spent) fuel has an enormous activity and emits penetrating γ radiation.
- Hot. The energy of these decays keeps heating the fuel even after the chain reaction has stopped (“decay heat”). Spent fuel must be cooled, or it can melt.
- Long-lived. Some fission products (and plutonium and other heavy nuclides made when U-238 absorbs neutrons) have half-lives of thousands to millions of years, so the waste stays hazardous for that long.
- Other waste: neutrons make structural materials radioactive; gloves, clothing and tools pick up contamination. These are lower-level wastes, handled separately.
HL Link to E.3: where fission fragments sit on the N–Z chart
The neutron-to-proton ratio of U-235 is \(143/92=1.55\). Kr-92 (\(56/36=1.56\)) and Ba-141 (\(85/56=1.52\)) keep almost the same ratio, but the stable nuclides of similar mass have far lower ratios (for example 1.33 for Kr-84 and 1.46 for Ba-138). The fragments therefore lie above the stability belt, which is why they decay by β− emission: each decay lowers N by one and raises Z by one. This is an application of the HL understanding in E.3; E.4 itself has no extra HL content.
The impact of long-term storage
- Timescale. The waste must be isolated from people and groundwater for many thousands of years — far longer than any human institution has existed. The storage must be safe without relying on future maintenance.
- Containment. High-level waste can be vitrified (set in glass), sealed in corrosion-resistant canisters and buried in geologically stable rock, so that multiple barriers prevent radioactive nuclides reaching groundwater.
- Responsibility and ethics. Future generations inherit the hazard without the benefit of the electricity. Choosing a site needs public consent; transport carries its own risk; stored plutonium raises security concerns (proliferation).
- Perspective. The volume of high-level waste is small compared with fossil-fuel waste (worked example 4 shows the mass of fuel is millions of times smaller), and it is contained rather than released into the atmosphere.
Exam tips for E.4
The commonest lost mark in E.4. The moderator slows down (reduces the kinetic energy of) neutrons by collisions; it does not absorb them. Control rods absorb neutrons; they do not slow them down. Write the verb, and say why: slow neutrons are more likely to cause fission of U-235; absorbing neutrons reduces the rate of fission.
The energy released is the difference between total binding energies, \(\sum A\times(\text{BE per nucleon})\). Subtracting binding energies per nucleon (e.g. 8.4 − 7.6 = 0.8 MeV) and stopping there gives an answer about 200 times too small. Use each nuclide's own nucleon number, and remember free neutrons contribute zero.
Put the incoming neutron on the left and every emitted neutron on the right. Keep 5–6 decimal places in the masses until the subtraction: the mass difference (about 0.2 u) is less than 0.1 % of the total mass (about 236 u), so rounding masses early destroys the answer.
A heat exchanger “transfers thermal energy from the coolant (primary circuit) to water in the secondary circuit, turning it into steam”. It does not “convert heat into electricity”, and it does not slow or absorb neutrons. Mention that keeping the circuits separate keeps radioactive coolant away from the turbine.
For “outline the problems of nuclear waste”, give a property and its consequence: highly radioactive → must be shielded; hot from decay → must be cooled; long half-lives → must be isolated for thousands of years. For “discuss”, give both sides and reach a judgement.
Common misconceptions
| Misconception | Why it is wrong | Correct idea |
|---|---|---|
| Energy is released because chemical bonds in the uranium are broken. | Chemical energies are a few eV per atom; fission releases about 200 MeV per nucleus. | The energy comes from the increase in nuclear binding energy, i.e. the decrease in rest mass. |
| The products have more mass because they are “more stable”. | More tightly bound nuclei have less mass per nucleon. | The products have less total mass; the mass decrease × c² is released. |
| Binding energy is energy stored in the nucleus and released when it splits. | Binding energy is the energy needed to separate a nucleus; more binding energy means less energy in the nucleus. | Energy is released because the products have more binding energy than the reactant. |
| Fast neutrons are best at causing fission, so the moderator speeds them up. | U-235 is far more likely to absorb a slow neutron; fast neutrons tend to pass through or be captured by U-238. | The moderator slows neutrons to thermal energies. |
| A nuclear power station can explode like a nuclear bomb. | Reactor fuel is only a few per cent U-235 and the reaction is kept critical, not supercritical. | Reactor accidents involve overheating and release of radioactive material, not a nuclear explosion. |
| Spent fuel stops being dangerous when the reactor is switched off. | Fission products keep decaying, emitting radiation and heat. | Spent fuel must be cooled and shielded for years and isolated for thousands of years. |
How this topic connects
Where the energy of a fission goes: kinetic energy first
Almost all of it first appears as kinetic energy. Typical shares of the roughly 200 MeV per U-235 fission: about 168 MeV as kinetic energy of the two fragments, which repel each other electrically; about 5 MeV as kinetic energy of the neutrons; about 7 MeV as prompt γ-ray photons; and, later, about 8 MeV from β particles, 7 MeV from γ rays and 12 MeV carried by antineutrinos as the fragments decay. The fragments travel less than a millimetre in the fuel, transferring their kinetic energy to the random motion of the surrounding atoms — internal (thermal) energy of the fuel (B.1). The antineutrinos escape, so about 195 of the 207 MeV is recovered as thermal energy.
From binding energy to reactor power output
The increase in total binding energy in one fission gives the energy per fission (worked example 3, about 200 MeV for U-235). The thermal power is then (fissions per second) × (energy per fission), and the rate of fission is set by the neutron population, which the control rods regulate. Turning it round, a required power output fixes the fission rate and the mass of fuel used each day (worked example 4: 3.16 kg of U-235 for 3.00 GW). Energy, power and efficiency are from A.3.
Nuclear fission and climate change: weighing the case for and against
For: fission produces no CO2 during operation, so over its life cycle a nuclear station emits far less greenhouse gas per unit of electrical energy than coal or gas (B.2); its enormous energy density means small fuel volumes; and it provides steady output whatever the weather, complementing wind and solar. Against: high-level waste must be isolated for thousands of years; accidents, though rare, can contaminate large areas; plants are expensive and slow to build, so they may cut emissions later than cheaper renewables; and fissile material raises security concerns. A balanced conclusion: fission can make a significant low-carbon contribution, but whether it should depends on economic, social and ethical judgements as well as physics — science can inform the decision but cannot make it alone.
Tools & NOS — risk, ethics and modelling
- Ethics (NOS): the same physics gave both nuclear weapons and nuclear power. Scientists working on fission in the 1940s had to weigh their responsibility for how their work would be used — a recurring question whenever science has powerful applications.
- Risk and evidence: public perception of nuclear risk often differs from measured risk (deaths or dose per unit of energy produced). Comparing technologies fairly needs data over the whole life cycle — mining, operation, waste and accidents.
- Exponential models (Tools): both the chain reaction (\(N_0k^n\)) and the decay of waste (E.3) are exponential processes. A spreadsheet that iterates the generations shows how sensitive the neutron population is to small changes in \(k\).
- Energy accounting (Tools): a Sankey diagram drawn to scale makes the 34 % efficiency and the large thermal transfer to the cooling water obvious at a glance.
Key equations
| Equation | Use | In data booklet? |
|---|---|---|
| \(E=mc^2\) | energy released from the mass decrease | yes (E.3) |
| 1 u = 1.661 × 10−27 kg = 931.5 MeV c−2 | mass in u × 931.5 = energy in MeV | yes (constants) |
| \(\Delta m=m_{\text{before}}-m_{\text{after}}\) | mass decrease in a fission reaction | no — from the definition |
| \(E=\sum\text{BE}_{\text{products}}-\sum\text{BE}_{\text{reactants}}\); BE = A × BE per nucleon | energy released from binding energies | no — from the definition |
| \(P=(\text{fissions per second})\times(\text{energy per fission})\) | thermal power of a reactor | no — from \(P=\dfrac{\Delta W}{\Delta t}\) (A.3) |
| \(\eta=\dfrac{\text{useful power out}}{\text{total power in}}\) | efficiency of the power station | yes (A.3) |
Check your understanding
1. Each fission of U-235 releases 200 MeV. Calculate the energy released by the fission of 1.0 kg of U-235 and compare it with burning 1.0 kg of coal (30 MJ kg−1).
Nuclei in 1.0 kg \(=\dfrac{1.0}{235\times1.661\times10^{-27}}=2.56\times10^{24}\). Energy \(=2.56\times10^{24}\times3.20\times10^{-11}=8.2\times10^{13}\ \text{J}\) — about \(2.7\times10^{6}\) times the 30 MJ from 1 kg of coal.
2. A fission reaction releases 180 MeV. Calculate the decrease in mass, in u and in kg.
\(\Delta m=\dfrac{180}{931.5}=0.193\ \text{u}\); \(0.1932\times1.661\times10^{-27}=3.21\times10^{-28}\ \text{kg}\).
3. State the difference between the role of the moderator and the role of the control rods, and explain what an operator does to reduce the power output.
The moderator slows neutrons down (so they are more likely to cause fission of U-235); the control rods absorb neutrons. To reduce the power, the control rods are inserted further, absorbing more neutrons, so fewer fissions occur per second.
4. A reactor contains 2000 neutrons in one generation and each generation has 0.97 times as many neutrons as the one before. Calculate the number after 30 generations and state whether the reactor is critical, subcritical or supercritical.
\(2000\times0.97^{30}=802\) neutrons (about 800). Fewer than one neutron per fission goes on to cause another fission, so the reactor is subcritical and the chain reaction dies away.
5. Explain why spent fuel is stored under water for several years after it is removed from a reactor.
The fission products are highly radioactive. Their decay releases energy, so the fuel keeps heating up; the water removes this thermal energy and prevents the fuel from overheating. The water also absorbs radiation (shielding), protecting workers. After several years the short-lived products have decayed, and the fuel can be moved to dry storage.
Practise E.4 with exam-style questions
Original Paper 1A, 1B and 2 questions on fission, with full mark schemes. Tick the questions you want and print them as your own test.
Revise and explore
- Flashcards — choose IB Physics and filter to E.4 Fission. Free, no sign-up.
- E.4 Fission chain reaction simulation
- E.4 Binding energy curve simulation
- Full IB Physics question bank (all sub-topics, SL & HL)
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