Historical Context & Motivation
The story of nuclear fission begins with a puzzle that captivated physicists in the 1930s. Scientists had been bombarding elements with neutrons, expecting to create heavier elements beyond uranium. Instead, they found something completely unexpected — the heavy nucleus was splitting apart into lighter fragments and releasing a staggering amount of energy. This discovery fundamentally changed our understanding of nuclear physics, and it carries enormous implications for both energy production and global security that persist to this day.
These discoveries raised a profound question: how does a single neutron cause an enormous nucleus to break apart, and why does this process release so much more energy than any chemical reaction? To answer this, we need to understand the forces that hold a nucleus together — and the conditions under which those forces can be overcome.
Core Principles of Nuclear Fission
Nuclear fission is the process in which a heavy, unstable nucleus absorbs a neutron and splits into two or more lighter nuclei, called fission fragments, along with additional free neutrons and a tremendous amount of energy. To appreciate why this works, you need to understand several interconnected ideas about how nuclear binding energy varies with mass number.
Binding Energy per Nucleon
Mass Defect and E = mc²
Induced vs. Spontaneous Fission
Chain Reactions
Fissile vs. Fissionable
The Fission Process — Visual Explanation
The diagram above illustrates the liquid drop model of fission, proposed by Niels Bohr and John Archibald Wheeler. When U-235 absorbs a thermal neutron, it momentarily becomes U-236 in a highly excited state. The nucleus begins oscillating — stretching into an elongated shape, much like a vibrating water droplet. As it stretches, the strong nuclear force (short-range, attractive) weakens across the neck region, while the Coulomb repulsion (long-range, repulsive between protons) grows dominant. Eventually the nucleus snaps apart at the neck, producing two unequal fission fragments, free neutrons, and energy.
Mathematical Framework
The energy released in fission can be calculated using two related approaches: through the mass defect and Einstein's mass–energy equivalence, or through the binding energy per nucleon curve. Both methods give the same answer, and the IB expects you to be comfortable with either.
The approximately 200 MeV released per fission event is distributed as follows: about 170 MeV goes into the kinetic energy of the fission fragments, approximately 5 MeV into neutron kinetic energy, about 15 MeV into gamma radiation, and the remainder into beta particles and neutrinos from the radioactive decay of fission products. In a reactor, the kinetic energy of the fragments is converted to thermal energy through collisions with surrounding atoms.
The Binding Energy per Nucleon Curve
The binding energy per nucleon curve is arguably the single most important graph in nuclear physics. It explains why fission of heavy nuclei and fusion of light nuclei both release energy, and why iron-56 sits at the peak of nuclear stability. For fission, the key insight is that nuclei to the right of the peak (A > 56) have lower binding energy per nucleon; splitting them into fragments closer to the peak releases the difference as kinetic energy.
Notice how the curve is relatively flat for medium and heavy nuclei (A > 30). This means that the energy released per nucleon in fission (about 0.9 MeV) is much less than the energy released per nucleon in fusion of very light nuclei (which can exceed 6 MeV per nucleon for hydrogen fusion). However, fission is far easier to achieve on Earth because it only requires a single neutron to trigger, whereas fusion requires overcoming immense Coulomb barriers by heating fuel to millions of degrees.
Worked Example — Energy Released in Fission
Let us calculate the energy released when a U-235 nucleus undergoes fission via the following reaction:
Nuclear Reactors — Components and Control
A nuclear fission reactor is an engineered system designed to sustain a controlled chain reaction at k = 1 (the critical state). The IB syllabus expects you to understand the role of each key component and how they work together to maintain safe, steady energy output. The table below summarizes the main reactor components.
| Component | Material Example | Function |
|---|---|---|
| Fuel | Enriched uranium (3–5% U-235) or plutonium-239 | Provides the fissile nuclei that undergo chain-reaction fission when they absorb neutrons. |
| Moderator | Water (H₂O), heavy water (D₂O), or graphite | Slows fast neutrons to thermal speeds (~0.025 eV) through elastic collisions, greatly increasing the probability that they will be absorbed by U-235. |
| Control Rods | Boron, cadmium, or hafnium | Absorb excess neutrons. Inserting rods deeper reduces k below 1 (subcritical); withdrawing them increases k. This is the primary method of controlling reactor power. |
| Coolant | Water, liquid sodium, or CO₂ gas | Transfers thermal energy from the reactor core to a heat exchanger or steam generator. In many designs, the coolant also serves as the moderator. |
| Shielding | Concrete, steel, lead | Absorbs gamma rays and neutrons that escape the core, protecting workers and the environment from ionizing radiation. |
Fission vs. Fusion — Connections to Advanced Theory
Both fission and fusion release energy by moving nuclei toward the peak of the binding energy per nucleon curve at iron-56. However, the two processes approach this peak from opposite directions, involve very different conditions, and present distinct engineering challenges. The IB syllabus treats both in Option E, and understanding their comparison deepens your grasp of both.
| Feature | Fission | Fusion |
|---|---|---|
| Definition | Heavy nucleus splits into lighter fragments | Light nuclei combine to form a heavier nucleus |
| Fuel | U-235, Pu-239 (rare, requires mining and enrichment) | Hydrogen isotopes — deuterium and tritium (abundant) |
| Energy per nucleon | ≈ 0.9 MeV per nucleon | ≈ 3–7 MeV per nucleon (much higher) |
| Conditions | Requires slow neutron capture; achievable at room temperature | Requires temperatures > 10⁷ K to overcome Coulomb barrier |
| Radioactive waste | Produces long-lived radioactive fission products (half-lives up to millions of years) | Produces minimal long-lived waste; main product (helium) is stable |
| Current status | Mature technology — hundreds of reactors operating worldwide | Still experimental — sustained net energy gain not yet achieved commercially |
| Direction on BE/A curve | Heavy nuclei move LEFT toward Fe-56 peak | Light nuclei move RIGHT toward Fe-56 peak |
As you continue through Option E of the IB Physics syllabus, you will encounter fusion in greater detail (E.4 also addresses it). The key connection is that both processes are explained by the same binding energy curve. Understanding fission thoroughly provides the foundation for understanding fusion — and for evaluating the complex trade-offs involved in choosing energy sources for the future. Questions about nuclear waste management, nuclear proliferation, and safety are also explored in the IB curriculum as part of the broader societal implications of nuclear physics.
Practice Problems
Lesson Summary
Nuclear fission is the splitting of a heavy nucleus (such as uranium-235) into two lighter fission fragments, 2–3 free neutrons, and approximately 200 MeV of energy. The energy comes from the mass defect — the small difference in total mass between reactants and products — converted to energy via E = Δm × c². On the binding energy per nucleon curve, fission moves heavy nuclei toward the iron-56 peak, where nucleons are most tightly bound.
In a nuclear reactor, the chain reaction is sustained at a critical state (k = 1) using control rods to absorb excess neutrons, a moderator to slow neutrons to thermal speeds, and a coolant to carry thermal energy to generators. Fission differs from fusion in that it splits heavy nuclei rather than combining light ones, but both processes release energy because they move nuclei toward greater binding energy per nucleon.