IB Physics HLTopic 5 — The Atomic & Nuclear WorldPaper 1 & 2split the heavy nucleus~16 min read
Spontaneous & Induced Fission
A big, heavy nucleus like uranium is a bit like an overloaded shelf — it’s barely holding itself together. Fission is when that nucleus splits into two smaller pieces, releasing a burst of energy. Sometimes it splits all on its own (spontaneous), and sometimes we make it split by firing a neutron at it (induced). That second kind is what powers every nuclear reactor on Earth — and once you see how one split can trigger the next, the whole idea of a chain reaction clicks into place.
📚 What you need to know
Fission is the splitting of a large nucleus into two smaller (daughter) nuclei, releasing energy
Spontaneous fission: a heavy nucleus splits on its own, with no trigger — this is rare
Induced fission: a nucleus absorbs a slow neutron, becomes unstable, then splits
Fission releases energy because the products have a higher binding energy per nucleon than the original
Each fission also releases 2 or 3 neutrons, which can trigger further fissions
A chain reaction happens when released neutrons go on to cause more fissions
A critical mass is the minimum mass needed to sustain a chain reaction
Energy is found from the mass defect using ΔE = Δmc2
What is fission?
Fission means a heavy, unstable nucleus splitting into two smaller nuclei of roughly similar size, plus a few spare neutrons and a lot of energy. The two smaller nuclei are called the daughter nuclei (or fission fragments). This only happens easily for very large nuclei — the ones near the far end of the periodic table, like uranium and plutonium.
The reason it releases energy is the binding energy per nucleon curve you met earlier. Very heavy nuclei sit lower on that curve than medium-sized ones. So when a heavy nucleus splits into two medium ones, the pieces are held together more tightly — and that jump in binding energy is released as kinetic energy of the fragments.
Here’s the trick to remembering which way energy flows: fission releases energy only when it moves nuclei towards the peak of the binding-energy-per-nucleon curve (around iron). Heavy nuclei are to the right of the peak, so splitting them climbs the curve — energy out. That’s the same peak that tells you why fusion works for light nuclei. One curve explains both.
Spontaneous vs induced fission
There are two ways to get a nucleus to split:
Spontaneous fission
Occasionally a very heavy nucleus simply splits by itself, with nothing hitting it. No trigger, no incoming particle — it’s just so unstable that it falls apart. This is very rare and slow, because most of the time these nuclei prefer to decay by alpha emission instead. You can think of spontaneous fission as a form of radioactive decay: it’s random and you can’t predict exactly when a given nucleus will go.
Induced fission
This is the useful one. We fire a slow-moving (thermal) neutron at a heavy nucleus such as uranium-235. The nucleus absorbs the neutron, becoming an even heavier, wobbling, unstable version of itself. Within an instant it splits into two daughter nuclei and throws out 2 or 3 more neutrons. Because we caused it by supplying the neutron, it’s called induced.
A slow neutron is absorbed by U-235, making unstable U-236, which stretches and then splits into two daughter nuclei, three neutrons and a burst of energy.
A typical fission reaction
Uranium-235 is the classic example. When it absorbs a neutron, one possible split is into barium and krypton:
Notice the bookkeeping, which examiners always check: the top numbers (mass numbers) balance — 1 + 235 = 236 on the left, and 141 + 92 + 3 = 236 on the right. The bottom numbers (atomic numbers) balance too — 0 + 92 = 92, and 56 + 36 + 0 = 92. The split isn’t always into Ba and Kr; a heavy nucleus can break up many different ways, but the totals must always balance.
A really common exam question just hands you a fission equation with one number missing and asks you to fill it in. Don’t panic — just balance the top row and the bottom row separately, like two little sums. The mass numbers on the left must equal the mass numbers on the right, and the same for the atomic numbers. That’s it.
WE 1
A uranium-235 nucleus absorbs a neutron and splits as: 10n + 23592U → 14156Ba + 9236Kr + 310n. Using the nuclear masses below, find the energy released, in MeV. (mn = 1.008665 u, mU = 235.043930 u, mBa = 140.914411 u, mKr = 91.926156 u, 1 u = 931.5 MeV c−2)
Step 1 — total mass beforembefore = 1.008665 + 235.043930 = 236.052595 uStep 2 — total mass after (3 neutrons!)mafter = 140.914411 + 91.926156 + 3(1.008665)mafter = 235.866562 uStep 3 — mass defectΔm = 236.052595 − 235.866562 = 0.186033 uStep 4 — convert to energyE = 0.186033 × 931.5≈ 173 MeV releasedThe mass “lost” became energy. Remember to count all 3 product neutrons in the after-mass — forgetting them is the classic slip. With 1 u = 931.5 MeV you skip the Δmc² arithmetic entirely.
The chain reaction
Here’s the clever part. Each fission spits out 2 or 3 fresh neutrons. If even one of those neutrons goes on to strike another uranium nucleus and cause it to fission, the process keeps itself going. That’s a chain reaction: fission produces neutrons, those neutrons cause more fissions, which produce even more neutrons, and so on.
If each fission triggers three more, the count grows 1 → 3 → 9 → 27… This runaway growth is what makes a chain reaction so powerful.
Fission occurs
releases 2–3 neutrons
Neutrons hit more nuclei
cause more fission
Chain reaction
Critical mass
A chain reaction only sustains itself if enough neutrons actually hit other nuclei instead of escaping. In a small lump of uranium, most neutrons shoot straight out of the surface before finding a nucleus — the reaction fizzles out. Make the lump bigger and neutrons are far more likely to be captured before escaping.
The critical mass is the minimum mass of fuel needed so that, on average, at least one neutron from each fission goes on to cause another fission. Below it (subcritical) the reaction dies out; at or above it the chain reaction is self-sustaining.
Too small and neutrons leak out before hitting anything (subcritical). Reach the critical mass and enough neutrons are captured to keep the reaction going.
WE 2
Estimate the energy released when 1.0 g of uranium-235 undergoes complete fission, taking each fission to release 200 MeV. Compare it to burning 1.0 g of coal, which releases about 24 kJ. (NA = 6.02 × 1023 mol−1, 1 MeV = 1.6 × 10−13 J)
Step 1 — number of U-235 nuclei in 1.0 gN = (1.0 ÷ 235) × 6.02×10²³ = 2.56×10²¹Step 2 — energy per fission in joules200 MeV = 200×10⁶ × 1.6×10⁻¹⁹ = 3.2×10⁻¹¹ JStep 3 — total energyE = 2.56×10²¹ × 3.2×10⁻¹¹ ≈ 8.2×10¹⁰ J≈ 8.2 × 1010 J from 1 gThat’s about 3 million times the energy of the same mass of coal. This staggering ratio is exactly why nuclear fuel is so energy-dense — a tiny amount of mass releases an enormous amount of energy.
⚛ Working a fission energy question
Balance the equation first: top numbers and bottom numbers each sum equal on both sides.
Mass before = neutron + heavy nucleus.
Mass after = both daughters + all the released neutrons.
Mass defectΔm = mass before − mass after.
Energy: multiply by 931.5 for MeV, or use ΔE = Δmc2 for joules.
💡 Top tips
Spontaneous = no trigger; induced = we fire a neutron in.
Fission releases energy because products have higher binding energy per nucleon.
Always count every product neutron in the after-mass.
Balance mass numbers and atomic numbers — two separate sums.
Critical mass = minimum mass for a self-sustaining chain reaction.
⚠ Common mistakes
Forgetting the extra neutrons when adding up the product mass
Saying fission needs a fast neutron — it’s usually a slow (thermal) one
Confusing spontaneous (no trigger) with induced (neutron fired in)
Thinking energy comes from “breaking bonds” — it comes from the mass defect
Mixing up fission (splitting heavy nuclei) with fusion (joining light ones)
Quick recap:Fission splits a heavy nucleus into two daughters plus neutrons and energy. Spontaneous happens on its own; induced is triggered by an absorbed neutron. Energy comes from the mass defect (ΔE = Δmc2) as products climb the binding-energy curve. The spare neutrons can drive a chain reaction, which sustains itself once the fuel reaches its critical mass.
Fission splits heavy nuclei apart to release energy — but there’s a mirror-image process that joins light nuclei together and releases even more. It’s what powers the Sun, and it sits on the opposite side of that same binding-energy peak. Next page: Nuclear Fusion.
Fission and chain reactions still tricky?
Book a free meeting and we’ll drill balancing fission equations, the mass-defect energy calculation, and the chain-reaction and critical-mass reasoning examiners love.
