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Every A-Level board uses this topic for a multi-step mass–energy calculation and at least one explanation marked on precise wording (“binding energy per nucleon increases, so...”). AQA, OCR and the Welsh boards add a thermal-reactor question, often as a 6-mark extended response. The arithmetic is easy to get right if you work in atomic mass units and MeV and keep track of electrons and free neutrons.
By the end you’ll be able to
Calculate mass defect and binding energy using E = mc² with u and MeV (1 u ≙ 931.5 MeV)
Interpret the binding energy per nucleon curve to explain why fission and fusion release energy
Calculate energy released in fission and fusion reactions from masses
Explain chain reactions, critical mass and the roles of moderator, control rods and coolant in a thermal reactor
Discuss the conditions needed for fusion and the handling of radioactive waste
What the exam asks
Define mass defect and binding energy, and calculate them with E=mc2 or 1u≡931.5MeV.
Calculate binding energy per nucleon and use the curve to explain why fission of heavy nuclei and fusion of light nuclei both release energy.
Find the energy released in a fission or fusion reaction, either from masses or from binding energies read off a graph.
Explain a chain reaction, critical mass, and the roles of the moderator, control rods and coolant in a thermal reactor, including the choice of materials.
Explain why fusion needs very high temperature and density, and discuss waste and safety.
Core ideas
Mass defect and binding energy
The mass of a nucleus is always less than the total mass of its separate protons and neutrons. The difference is the mass defect:
Δm=Zmp+(A−Z)
vii.Check your understanding
3 questions on mass defect, binding energy, fission and fusion. Every option is explained once you answer.
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PromptCard 1 of 3
Define mass defect.
2
Δ
m
OCR A (6.4.4) and OCR B: mass defect, binding energy per nucleon, induced fission, the chain reaction and moderator, control rods, environmental impact of waste, and conditions for fusion.
Cambridge 9702 (topic 23): mass defect, binding energy and energy-release calculations, but no reactor design. If your data sheet gives the atomic mass unit only in kilograms (1.66×10−27 kg), convert with E=mc2.
Eduqas, WJEC and CCEA: the same mass–energy calculations and the binding energy per nucleon curve, with qualitative fission and fusion.
m
n
−
mnucleus
The binding energy is the energy needed to separate a nucleus completely into its individual protons and neutrons. It equals the energy released when the nucleus forms from them:
EB=Δmc2
Binding energy is not energy stored inside the nucleus. A nucleus with a large binding energy has less mass-energy than its parts; it sits deeper in an energy well.
Units.1u=1.661×10−27 kg, which is equivalent to 931.5 MeV. Working in u and MeV avoids powers of ten: energy in MeV = mass in u × 931.5. To convert MeV to joules, multiply by 1.60×10−13.
Particle
Mass / u
proton
1.00728
neutron
1.00867
electron
0.00055
Binding energy per nucleon
Dividing EB by the nucleon number A measures how tightly each nucleon is held, so it measures stability.
The curve rises steeply for light nuclei, with helium-4 unusually high (about 7.1 MeV) compared with its neighbours.
It peaks at about 8.8 MeV near iron-56 and nickel-62, the most stable nuclei.
It falls slowly for heavy nuclei, to about 7.6 MeV for uranium-235, because the growing electrostatic repulsion between protons acts over the whole nucleus while the short-range strong force acts only between neighbours.
Any change that moves nucleons towards the peak increases the total binding energy. The products then have less mass than the reactants, and the difference is released as kinetic energy (and γ photons):
energy released=(total EB of products)−(total EB of reactants)=Δmc2
Fission: a heavy nucleus (A>56) splits into two medium nuclei.
Fusion: light nuclei join to make a heavier one (A<56). The curve is much steeper on the light side, so fusion releases more energy per nucleon (about 3.5 MeV per nucleon for D–T compared with about 0.85 MeV per nucleon for U-235 fission).
Induced fission and the chain reaction
A uranium-235 nucleus absorbs a neutron, forms unstable uranium-236, and splits into two neutron-rich fragments plus 2 or 3 fast neutrons, releasing about 200 MeV:
92235U+01n→56141Ba+3692Kr+301n
Most of the energy appears as kinetic energy of the fragments, which becomes internal energy of the fuel. If at least one neutron from each fission goes on to cause another fission, the reaction is a chain reaction. The critical mass is the minimum mass of fuel for a self-sustaining chain reaction. Below it, too many neutrons escape through the surface, because a small lump has a large surface area compared with its volume.
The thermal reactor
Part
Job
Typical material and why
Fuel rods
contain enriched uranium (a few % U-235)
spread out so heat is removed evenly
Moderator
slows fast (about 2 MeV) neutrons to thermal speeds (about 0.025 eV), where U-235 is far more likely to absorb them
water, heavy water or graphite: nuclei of low mass, so a neutron loses a large fraction of its KE in each elastic collision, and they absorb few neutrons
Control rods
absorb neutrons, so that on average exactly one neutron per fission causes another fission
boron or cadmium: very good neutron absorbers; lowered further to reduce power
Coolant
carries thermal energy to the heat exchanger and turbines
water or carbon dioxide gas: high specific heat capacity, flows easily, low neutron absorption
Shielding
absorbs neutrons and γ
a steel pressure vessel inside thick concrete
Why low-mass moderator nuclei? In a head-on elastic collision between a neutron (mass m) and a stationary nucleus of mass M, the neutron keeps a fraction (M+mM−m)2 of its kinetic energy. For carbon-12 this is (11/13)2=0.72. For hydrogen it can be almost zero. Lead would hardly slow the neutron at all.
Safety. An emergency shut-down drops all the control rods fully into the core. Spent fuel is the most hazardous waste: the neutron-rich fission products emit β− and γ radiation, some have long half-lives, and they keep producing heat. Spent fuel is handled remotely and cooled under water, then sealed (for example vitrified in glass inside steel) for long-term deep geological storage. Low-level waste such as contaminated clothing is compacted and buried in sealed containers.
Fusion conditions
Nuclei are positively charged, so they repel. To fuse, they must get close enough (a few femtometres) for the strong force to act. This needs:
a very high temperature (about 108 K in a reactor), so that nuclei have enough kinetic energy to overcome the electrostatic repulsion;
a high density, so that collisions happen often enough for the power output to be useful;
confinement for long enough, which in a tokamak means strong magnetic fields, because no material container survives contact with the plasma.
The Sun’s core is only about 1.5×107 K. Fusion still happens because a few nuclei in the high-energy tail of the speed distribution, helped by quantum tunnelling, get through the barrier, and the core contains an enormous number of nuclei.
Worked examples
Exam technique
Lay out mass calculations as “mass before, mass after, difference”. Keep 5–6 decimal places in u until the end, because the answer comes from subtracting two nearly equal numbers.
Atomic or nuclear masses? In reactions, atomic masses are fine when the proton numbers balance. For the binding energy of a single nucleus, either subtract the electrons from an atomic mass or use the mass of a hydrogen atom (1.00783 u) in place of mp.
Energy released is a positive number. Say “energy is released because the total binding energy increases” or “because the total mass decreases”. Never say “because binding energy is released”.
Reactor 6-markers: give each component’s job, how it does it (elastic collisions, neutron absorption, heat transfer), why the material suits it, then add safety. Link control rods to “exactly one further fission per fission” (a steady chain reaction).
Estimate questions: use “about 200 MeV per fission” and N=A×1.661×10−27kgm to scale up to a kilogram of fuel.
Common mistakes
Quick recap
Mass defect = mass of separate nucleons − mass of nucleus. Binding energy = Δmc2 = the energy to pull the nucleus completely apart.
1u≡931.5 MeV, and 1MeV=1.60×10−13 J.
Binding energy per nucleon peaks at about 8.8 MeV near iron-56. Moving towards the peak (fission of heavy nuclei, fusion of light ones) releases energy.
Energy released = increase in total binding energy = decrease in mass × c2.
Thermal reactor: the moderator slows neutrons by elastic collisions with light nuclei, control rods absorb neutrons to keep one fission per fission, and the coolant removes heat.
Fusion needs a high temperature (to overcome electrostatic repulsion), a high density (collision rate) and confinement.