IB Physics SLTopic 5 — The Atomic & Nuclear WorldPaper 1 & 2balance A and Z~8 min read
Decay Equations
A decay equation is just balanced bookkeeping for the nucleus. Whatever the nucleus starts with in nucleons and protons, the totals on both sides of the arrow must match — nothing appears or vanishes. Get that one idea and you can predict the daughter nucleus of any alpha, beta, or electron-capture decay in seconds.
📘 What you need to know
In every decay equation, the nucleon numbers (A) balance and the proton numbers (Z) balance across the arrow
Alpha decay: A decreases by 4, Z decreases by 2 (a helium nucleus leaves)
Beta-minus decay: A stays the same, Z increases by 1 (a neutron becomes a proton, emitting an electron + antineutrino)
Beta-plus decay: A stays the same, Z decreases by 1 (a proton becomes a neutron, emitting a positron + neutrino)
Electron capture: A stays the same, Z decreases by 1 (the nucleus absorbs an inner electron)
The decay type is set by why the nucleus is unstable: too many neutrons → β−; too many protons → β+ or capture; too many nucleons → α; too much energy → γ
Decays can be plotted on an N–Z graph, where each type shifts the nucleus in a characteristic direction
The Golden Rule: Balance Both Numbers
Every nucleus is written AZX, with the nucleon numberA on top and the proton numberZ below. In a decay equation, add up the top numbers on the left and they must equal the top numbers on the right; do the same for the bottom numbers. This works because nucleons and charge are both conserved.
Conservation across the arrow
sum of A (left) = sum of A (right) & sum of Z (left) = sum of Z (right)
Each emitted particle has its own top and bottom numbers to include in the sum: an alpha is 42α, a beta-minus is 0−1β, a beta-plus is 0+1β, and a gamma is 00γ.
Why Each Decay Happens
A nucleus doesn’t pick a decay at random — the type depends on what’s making it unstable. This is the quickest way to know which equation to write.
🧭 Which decay, and why
Too many neutrons → beta-minus: a neutron turns into a proton, firing out an electron and an antineutrino
Too many protons → beta-plus or electron capture: a proton turns into a neutron
Too many nucleons (heavy nucleus) → alpha: a helium nucleus is ejected
Too much energy → gamma: a photon carries off the excess (usually after another decay)
Alpha Decay
The nucleus ejects a helium nucleus, so it loses 4 nucleons and 2 protons. The daughter is a different element, sitting two places back on the periodic table.
Alpha decayAZX → A−4Z−2Y + 42α
A − 4
and
Z − 2
→
new element, 2 back
Beta-Minus Decay
Inside a neutron-heavy nucleus, a neutron converts into a proton, throwing out a fast electron (the beta-minus particle) and an antineutrino. No nucleons are lost, so A is unchanged, but gaining a proton pushes Z up by 1.
Beta-minus decayAZX → AZ+1Y + 0−1β + v̅e
Beta-Plus Decay & Electron Capture
In a proton-heavy nucleus, a proton converts into a neutron. It can do this in two ways. In beta-plus decay it emits a positron and a neutrino; in electron capture it instead pulls in one of the atom’s own inner electrons. Either way the nucleon number stays the same and Z drops by 1.
Beta-plus decayAZX → AZ−1Y + 0+1β + ve
Electron captureAZX + 0−1e → AZ−1Y + ve
Seeing Decays on an N–Z Graph
Plot neutron number N up the side and proton number Z along the bottom, and each decay becomes an arrow pointing in a fixed direction. This is a favourite exam diagram, so learn the three moves.
Each decay moves the nucleus a fixed way on the N–Z map: alpha down-left (N−2, Z−2), beta-minus down-right (N−1, Z+1), beta-plus up-left (N+1, Z−1).
Quick recap: balance A and Z across the arrow. Alpha: A−4, Z−2. Beta-minus: A same, Z+1. Beta-plus and electron capture: A same, Z−1. The instability tells you which one to use.
WE 1
Polonium-210, 21084Po, undergoes alpha decay. Write the full decay equation and identify the nucleon number and proton number of the daughter nucleus.
Apply the alpha rule (A−4, Z−2)
nucleon number: 210 − 4 = 206
proton number: 84 − 2 = 82 → this is lead (Pb)
Write and balance the equation21084Po → 20682Pb + 42α
check A: 210 = 206 + 4 ✓ check Z: 84 = 82 + 2 ✓daughter: A = 206, Z = 82
WE 2
Strontium-90, 9038Sr, is neutron-rich and undergoes beta-minus decay. (a) State what happens inside the nucleus. (b) Write the balanced decay equation, including the antineutrino.
Part (a) — inside the nucleus
a neutron changes into a proton
an electron (the β− particle) and an antineutrino are emitted
→ A stays 90, Z rises from 38 to 39 (yttrium)Part (b) — balanced equation9038Sr → 9039Y + 0−1β + v̅echeck A: 90 = 90 + 0 ✓ check Z: 38 = 39 + (−1) ✓daughter: 9039Y
💡 Top tips
Always check both balances at the end: top numbers add up, and bottom numbers add up (remember −1 for the beta-minus particle)
Beta-minus adds a proton (Z+1); beta-plus and electron capture remove one (Z−1). In all beta processes A stays the same
Don’t forget the neutrino: antineutrino (v̅e) with beta-minus, neutrino (ve) with beta-plus and capture
Gamma changes neither A nor Z — it just carries away excess energy, usually after another decay
⚠ Common mistakes
Confusing neutron number with nucleon number — in alpha decay A falls by 4 and Z by 2 (so N also falls by 2)
Getting the beta direction backwards: beta-minus raises Z, beta-plus lowers it
Leaving out the antineutrino or neutrino, or giving the wrong one for the decay type
Forgetting the beta particle’s bottom number is −1, which throws off the Z balance
Up next: Activity & Half-Life. You can now say what a nucleus turns into — next we look at how fast a whole sample decays, introducing activity, half-life, and reading decay curves.
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