Start here. Picture a long valley with steep walls. A marble high on either wall will roll down toward the bottom and release energy as it goes. Atomic nuclei behave the same way. There is a "most comfortable" size for a nucleus — around iron — that sits at the very bottom of the valley. A heavy nucleus like uranium sits high on one wall, so it can release energy by splitting into two medium pieces that slide downhill. A pair of light nuclei like hydrogen sit high on the other wall, so they release energy by fusing into a bigger one. Both moves head toward iron, and both let go of energy doing it.
Build the idea. The "height on the wall" is measured by the binding energy per nucleon, written $B/A$ — how tightly each proton and neutron is glued in, in MeV. Iron sits highest (most tightly bound, $\sim 8.8$ MeV per nucleon); uranium is looser ($\sim 7.6$). When particles end up more tightly bound, the leftover binding shows up as released energy. The bookkeeping is Einstein's $E = mc^2$: the products weigh a hair less than what you started with, and that missing mass — the mass defect $\Delta m$ — becomes the energy $Q = \Delta m\, c^2$.
Try one fusion sum. Deuterium (mass $2.0141$ u) plus tritium ($3.0160$ u) gives $5.0301$ u going in. Out come helium-4 ($4.0026$ u) and a neutron ($1.0087$ u), totalling $5.0113$ u. The difference is $\Delta m \approx 0.0189$ u, and since $1\,\text{u} = 931.5$ MeV, that releases $Q \approx 17.6$ MeV — exactly the D–T number on screen. Splitting one $^{235}$U gives about $200$ MeV the same way.
Go deeper. Why is fusion so much harder to start than fission? Both nuclei are positively charged, so they repel. A slow neutron has no charge, so it can drift into $^{235}$U and tip it over its fission barrier for free. But to fuse, two nuclei must be flung together hard enough to beat their Coulomb repulsion — that takes temperatures near $10^8$ K (tens of keV). For fission the key knob is the multiplication factor $k$: each split releases $\nu \approx 2.4$ neutrons, and the population grows as $N_n = N_0\, k^{\,n}$. If $k<1$ the chain dies; $k=1$ holds steady (a reactor); $k>1$ runs away (a bomb). For fusion the knob is the plasma temperature $T$, which sets the reactivity $\langle\sigma v\rangle$ — and you must also hold the plasma together long enough, the Lawson criterion.
Try this in the sim above. Switch to Chain Reaction and set $k$ below 1 — the neutrons fizzle out; nudge $k$ above 1 and watch the count explode generation by generation (compare it to the dashed $k^n$ line on the Generations graph). Then open D-T Fusion and drag the temperature $T$ up toward 70 keV — the $\langle\sigma v\rangle/\text{max}$ readout climbs and helium starts appearing. Finally open the Binding Energy Curve graph and find the iron peak: everything to its right releases energy by splitting, everything to its left by fusing.
Section 03
Equations & Derivation
Both fission and fusion convert a small fraction of mass into energy via $E=mc^2$. The driving quantity is the binding energy per nucleon $B/A$, which peaks near $A\approx 56$ (iron). Heavy nuclei release energy when they split toward this peak; light nuclei release energy when they merge toward it.
Approximately $n\tau_E T \gtrsim 3 \times 10^{21}$ keV·s/m³ for D-T at $T \sim 14$ keV.
Mapping to the simulation
Fission mode shows a single $^{235}$U event with daughter fragments and prompt neutrons. Chain mode tracks neutron generations with selectable $k$. Fusion mode shows D and T ions in a Maxwell-Boltzmann distribution at temperature $T$ — collision rate scales as $\langle\sigma v\rangle$, peaking near $T \approx 70$ keV.
Fission mode: a slow neutron strikes $^{235}$U, the compound nucleus deforms, splits into two unequal daughter fragments, and emits 2-3 fast neutrons. Chain mode: each fission's neutrons can trigger more fissions; the population grows or decays as $k^n$. Fusion mode: D and T ions move with thermal velocities; pair collisions occasionally produce $^4$He and a 14 MeV neutron when their kinetic energy overcomes Coulomb repulsion.
It's a competition between attractive short-range strong force (favors many neighbors → large nuclei) and repulsive long-range Coulomb force (favors small Z). For light nuclei, surface effects dominate; for heavy nuclei, Coulomb repulsion grows as $Z^2$. The two effects balance near $A \approx 56$ (Fe-56, Ni-62). Above this, splitting releases energy; below, fusing releases energy.
Fission powers ~10% of the world's electricity (444 reactors as of 2024) and atomic weapons. Fusion powers every star including our Sun (the proton-proton chain), hydrogen bombs (D-T fusion triggered by a fission primary), and is the goal of ITER, the National Ignition Facility (which achieved ignition in Dec 2022), tokamaks, and stellarators.
Fission of U-235 needs only a slow ($\sim 0.025$ eV) neutron — easy. Fusion requires positively-charged nuclei to overcome Coulomb repulsion ($\sim$ MeV of kinetic energy each) which means temperatures of $\sim 10^8$ K. Plus, the plasma must be confined long enough (Lawson criterion) — a triple challenge that has taken 70+ years and is just now being solved.
About 80% of fission's $\sim$ 200 MeV is in the kinetic energy of the fragments. Fragments slow within ~10⁻⁶ m of fission, depositing heat in the fuel. The fuel heats water/coolant; steam drives a turbine. The remaining 20% is in beta-decay of fission products (~7%), prompt neutrons (~5%), and gamma rays (~5%, ~3%).
No — and this is one of fusion's huge safety advantages. In a fusion plasma at $\sim 10^8$ K, any disruption (instability, loss of confinement) cools the plasma instantly, halting fusion. There is no chain reaction; each reaction needs the next collision, not a self-multiplying neutron flux.
U-235 has odd $N$. Adding a neutron makes U-236 with paired nucleons — much more bound. The pairing-energy gain ($\delta \sim 0.7$ MeV) plus binding from the captured neutron exceeds the fission barrier ($\sim 6$ MeV), making U-235 fissile by thermal neutrons. U-238 has even $N$; adding another neutron gives less pairing gain, so the resulting U-239 falls below the fission barrier — it needs a fast neutron.
Resources: Khan Academy; HyperPhysics; MIT OpenCourseWare; Paul's Physics Notes.
Section 05
Common Misconceptions
❌ Misconception: Fission and fusion both 'destroy' atoms and turn them into pure energy.
✅ Correction: Neither destroys the atoms — both rearrange nucleons. The total nucleon count is conserved (235+1 → 141+92+3, all ≥ 0). Only a tiny fraction of mass (~0.1% in fission, ~0.4% in D-T fusion) becomes energy via $E=mc^2$.
📖 Reference: Krane — Introductory Nuclear Physics, Wiley, §13.1 'Energetics of Fission' & §14.1 'Energetics of Fusion'.
❌ Misconception: Fission was discovered by splitting an atom with a hammer or particle accelerator.
✅ Correction: Fission was discovered by Hahn & Strassmann in 1938 using SLOW (thermal) neutrons. Lise Meitner and Otto Frisch interpreted the result — the U nucleus oscillates and splits like a charged liquid drop. Energetic projectiles are not needed; thermal energy suffices.
❌ Misconception: Fusion in stars is hot enough that nuclei smash together easily.
✅ Correction: At the Sun's core ($T \approx 1.5\times 10^7$ K $\approx 1.3$ keV), the average kinetic energy is far below the Coulomb barrier ($\sim$ MeV). Fusion proceeds only via quantum tunneling through this barrier — the reason stars burn for billions of years rather than seconds.
✅ Correction: Fission products are highly neutron-rich and undergo $\beta^-$ decay chains over seconds to centuries. This 'decay heat' is why a reactor cannot be shut off instantly — Fukushima's meltdowns came from this residual heat after SCRAM, not ongoing fission.
❌ Misconception: A nuclear bomb cannot fizzle — it always achieves full yield.
✅ Correction: Achieving high yield requires extremely fast assembly to supercritical mass before the chain reaction blows the fuel apart. Implosion timing of microseconds is required. A 'fizzle' (yield far below design) is a documented failure mode for primitive designs.
📖 Reference: Reed — The Physics of the Manhattan Project, Springer 2010, Ch. 7.
❌ Misconception: Cold fusion at room temperature has been demonstrated.
✅ Correction: The 1989 Fleischmann-Pons announcement could not be reproduced. Standard physics rules out conventional fusion at room temperature: the Coulomb barrier penetration probability is astronomically small ($e^{-100}$). Muon-catalyzed fusion is real but limited by muon lifetime and α-sticking.
📖 Reference: Huizenga — Cold Fusion: The Scientific Fiasco of the Century, Oxford 1993; APS 'cold fusion' position.
Misconception research: Coletta & Phillips — Am. J. Phys. 73 (2005); Hosson & Bouwens — 'Common student misconceptions in nuclear physics', PER review 2014; ANS Position Statement on radiation.