Intuition The ONE core ideaA heavy nucleus splitting releases spare neutrons, and fission keeps going only if enough of those neutrons survive to trigger the next split . Everything on this topic — energy released, the number k how many neutrons are born versus how many are lost .
This page builds the vocabulary before you meet the physics. If the parent note ever wrote a symbol you didn't recognise, it lives here. Read top to bottom: each item leans on the one above it.
Look at the figure. The nucleus is a bag of red balls (protons) and blue balls (neutrons) squeezed together. The picture matters because fission is literally this bag tearing into two smaller bags , and every quantity we compute counts these balls.
Intuition Why the bag stays together at allProtons all carry the same charge, and like charges push apart. So what stops the bag exploding? A separate, stronger, very short-range pull called the nuclear force that acts between any two touching nucleons. A heavy nucleus is a tug-of-war: electric push-apart vs. nuclear pull-together — barely balanced, which is exactly why a nudge can break it.
The parent note writes symbols like 92 235 U 0 1 n
Worked example Decoding the fission players
92 235 U Z = 92 A = 235 235 − 92 = 143 0 1 n A = 1 Z = 0 is the neutral nucleon.3 0 1 n
Z A Why it feels right: they look like formatting.
The fix: In every reaction the totals of A Z balance left and right — that's conservation of nucleons and charge. It's how you check a reaction is written correctly.
Z = 92 92 235 U + Z = 0 0 1 n ⟶ Z = 56 56 141 Ba + Z = 36 36 92 Kr + 3 0 1 n
Check the bottoms: 92 + 0 = 56 + 36 + 0 = 92 235 + 1 = 141 + 92 + 3 = 236
Definition Atomic mass unitu atomic mass unit , written u u 235 U 235 u
Definition The speed of lightc c c ≈ 3 × 1 0 8 exchange rate between mass and energy — see below.
See Mass-Energy Equivalence E=mc^2 for the full story of where this comes from.
Definition The electron-volt and MeVAn electron-volt (eV MeV is a million of them: 1 MeV = 1 0 6 eV = 1.6 × 1 0 − 13 J ≈ 200
Δ m Δ Δ m = m before − m after goes missing during fission. That missing mass reappears as the released energy Q Q = Δ m c 2
Definition Binding energy and BE per nucleonThe binding energy is the energy you'd have to pump in to pull a nucleus completely apart into free nucleons. Divide it by the number of nucleons A binding energy per nucleon (BE/A
Look at the curve. Higher up = more tightly bound = more stable . The peak sits near iron (A ≈ 56 A ≈ 235 lower , at ≈ 7.6 A ≈ 90 – 140 higher , at ≈ 8.5
Intuition Why the shape means fission releases energySplitting uranium moves you from a low point (loosely bound) to a higher point (tightly bound) on this curve. Getting more tightly bound means the system gives off the difference — like a ball rolling downhill into a deeper valley releases energy. That per-nucleon drop of ≈ 0.9 ≈ 235 ≈ 200
The full curve is its own topic: Binding Energy per Nucleon Curve . Note that Nuclear Fusion uses the left side of the same curve (light nuclei climbing up), which is why fusion also releases energy.
ν ν average number of new neutrons born in one fission. For 235 U ν ≈ 2.5
Definition A "generation"Group the fissions into rounds. All the fissions caused by this batch of neutrons form one generation ; the neutrons they release cause the next generation. It's like a family tree of splits.
Definition Multiplication factork k = neutrons in the previous generation neutrons in the new generation "does the neutron population grow, hold steady, or shrink each round?"
The three panels show all three cases the parent lists:
k < 1 subcritical ): each row is smaller — the tree withers and dies.k = 1 critical ): each row is the same size — steady, the reactor's normal mode.k > 1 supercritical ): each row is bigger — explosive growth.
Definition Powers and the exponentn k n k n k n k n N n = N 0 k n power — the engine of exponential growth.
ln k n = 2 n natural logarithm ln ln ( k n ) = n ln k n = ln k ln 2
Definition Generation timeτ τ real clock time between one generation and the next. For bare fast neutrons τ ∼ 1 0 − 8 effective τ ∼ 0.1 N ( t ) = N 0 k t / τ
Neutrons don't all survive to cause a fission — some leak out, some get absorbed uselessly. How likely a neutron is to hit and split a nucleus is set by the Neutron Cross-section . How long-lived unstable fragments hang around is Radioactive Decay and Half-life .
The critical-mass argument is pure geometry, so we need three shape facts.
R ∝ R 3 ∝ R 2 R
its volume (how much stuff fits inside) grows like R 3
its surface area (the skin) grows like R 2 ∝
Intuition Why surface-to-volume decides everythingNeutrons are made throughout the volume (∝ R 3 leak away through the surface (∝ R 2 production leakage ∝ R 3 R 2 = R 1 . small lump has a big 1/ R k < 1 R 1/ R 1/ R minimum (critical) mass exists.
ρ ρ mass packed per unit volume — how tightly the nuclei are crammed. Squeezing a lump (raising ρ R and puts nuclei closer so neutrons find a target sooner. That's why the parent notes M c ∝ 1/ ρ 2
Where all this bookkeeping is engineered on purpose, you get a Nuclear Reactor .
protons neutrons nucleons
binding energy per nucleon
mass energy E equals m c squared
radius volume surface density
surface over volume leakage
Every arrow says "you need the left box to understand the right box". All roads lead to the parent: the Fission topic .
Cover the right side and see if you can answer each before revealing.
In Z A X A Z A Z
How many neutrons are in 92 235 U A − Z = 235 − 92 = 143
What does Δ m The mass that goes missing in the reaction; it becomes energy via Q = Δ m c 2
Convert 1 u ⋅ c 2 931.5
What is BE per nucleon, and why does moving up the curve release energy? Binding energy divided by A
What does ν 235 U Average neutrons produced per fission; ≈ 2.5
Define k New-generation neutrons ÷ previous-generation; k < 1 k = 1 k > 1
Why is N n = N 0 k n power ? Each generation multiplies by k n n
Which tool solves k n = 2 n The natural log; n = ln 2/ ln k
How do volume and surface of a sphere scale with R Volume ∝ R 3 ∝ R 2
Why does leakage/production go like 1/ R Leakage ∝ R 2 ∝ R 3 R 2 / R 3 = 1/ R
What is ρ Density (mass per volume); higher ρ R M c ∝ 1/ ρ 2
