Key Idea: An unstable nucleus calms down by throwing out radiation — and this topic is the four things the IB asks about that. What the radiation is and how it behaves (α, β⁻, γ); how to balance a decay equation so the new nucleus falls out; how much energy the decay releases through E = mc²; and how fast a source weakens, measured by its half-life. It is examined on both papers. Paper 1A is quick multiple-choice — identify a radiation from how it penetrates or deflects, pick the daughter's A and Z, or halve a count rate over a whole number of half-lives. Paper 2 is longer structured work — a show that the released energy is about 5 MeV from a mass defect, a show that the alpha carries about 98% of it, completing a nuclear equation, or correcting a count rate for background.
📋 Key formulas & rules
Only one equation in this topic carries the data-booklet badge — E = mc². Everything else is a rule you memorise: how A and Z change in each decay, and the halving rule for half-life. The exponential decay law A = A₀e⁻λᵗ is not on the SL booklet, so at SL you only ever halve over whole half-lives.
- energy released in the decay, the disintegration energy Q (J, or MeV)
- mass defect Δm — the mass that disappears in the decay
- speed of light, 3.00 × 10⁸ m s⁻¹ (given constant)
- parent nuclide before decay (A on top = protons + neutrons, Z below = protons)
- daughter: nucleon number falls by 4, proton number by 2
- alpha particle = a helium-4 nucleus (2 protons + 2 neutrons)
- parent nuclide before decay
- daughter: nucleon number unchanged, proton number rises by 1
- beta-minus particle = an electron (made when a neutron becomes a proton)
- antineutrino — emitted with the electron (no charge, ≈ no mass)
- the activity (or count rate) after the time has passed
- the starting activity (or count rate)
- the number of WHOLE half-lives that have passed, n = total time ÷ half-life
- kinetic energy carried by the alpha (the light product)
- total energy released in the decay
- mass of the daughter (the heavy product)
- mass of the alpha (the light product)
☢️ The three radiations side by side
Going α → β → γ: penetration goes UP (paper → aluminium → lead) and ionising power goes DOWN (α strongest → γ weakest). The best ioniser travels the shortest distance — α dumps its energy fastest, so it is stopped first. And only γ (neutral) is not bent by a field.
⚖️ How A and Z change in each decay
The top numbers add up the same on both sides (nucleon number A conserved), and the bottom numbers add up the same (proton number Z conserved). That single check finds the daughter every time. For a chain of two decays, apply the changes one at a time and keep a running tally; use N = A − Z if asked for neutrons.
📉 Half-life vs energy — the two calculations
✏️ Worked exam-style questions
IB-style question — identify the radiation
An unknown radiation passes straight through a sheet of paper but is stopped by a 3 mm aluminium plate. When it crosses a magnetic field it is deflected. State which type of radiation it is, giving a reason from each observation.
Solution:
Use the penetration clues to narrow it down — paper does NOT stop it (so it is not the least-penetrating alpha), but a few mm of aluminium does (so it is not the very penetrating gamma, which needs lead):
Medium penetration ⇒ the radiation is beta-minus, OR could still be something charged — check the field clue.
It is DEFLECTED by a field, so it must carry a charge — gamma (neutral) would pass straight through undeflected.
Medium penetration AND charged points to one answer:
Beta-minus (β⁻). Paper does not stop it (not α), a few mm of aluminium does (not the lead-stopping γ), and it deflects in a field, so it is charged (not the neutral γ). Use penetration to narrow to two, then the deflection to decide.
IB-style question — balance a decay chain
Radium-226 (A = 226, Z = 88) emits an alpha particle, and the nucleus it forms then emits a beta-minus particle. Find the nucleon number, proton number AND neutron number of the FINAL nuclide.
Solution:
Alpha step — nucleon number falls by 4, proton number falls by 2:
Beta-minus step — nucleon number unchanged, proton number rises by 1:
Neutron number = nucleon number − proton number:
The final nuclide has A = 222, Z = 87 and N = 135 (it is francium-222). Apply each decay one at a time, keeping a running tally of A and Z, then use N = A − Z for the neutrons.
IB-style question — energy released, and the alpha's share
A nucleus at rest decays by alpha emission. The masses are: parent = 230.033130 u, daughter = 226.025410 u, alpha = 4.002600 u. (a) Show that the energy released is about 5 MeV. (b) The daughter has mass 226 u and the alpha 4 u — show that the alpha carries about 98% of that energy. (1 u = 931.5 MeV c⁻².)
Solution:
(a) Find the mass defect Δm = parent mass − total mass of the products:
(a) Turn the lost mass into energy with the given E = mc²; with Δm in u, the c² is built into 931.5, so just multiply:
(b) The parent is at rest, so the two products carry equal and opposite momentum. With KE = p²/2m, the alpha's share is the daughter's mass over the total mass:
(b) Evaluate as a percentage:
(a) Δm = 0.005120 u, so E = 0.005120 × 931.5 ≈ 4.77 MeV ≈ 5 MeV. (b) The alpha's share = 226 ÷ 230 ≈ 0.98 = 98%. Mass defect FIRST, then E = mc²; the light product (the alpha) always gets most of the energy. Keep every decimal place when subtracting the masses.
IB-style question — count rate after two half-lives
A detector near a fresh source reads 124 counts per second. With the source removed the background reads 4 counts per second. The source has a half-life of 15 minutes. Find the count rate the SAME detector reads after 30 minutes.
Solution:
Subtract the background FIRST to get the source's true count rate now:
Find the number of whole half-lives, n = total time ÷ half-life:
Halve the source rate n = 2 times — multiply by (½)² = ¼:
Add the background back on — the detector still records it:
The detector reads 34 counts per second after 30 minutes. Always subtract the background before halving, halve once per half-life (never subtract a fixed amount), then add the background back if the question wants the measured value.
🧠 Quick self-check
Tap each card to reveal the answer.
🎯 Exam tips
Exam Tips
- α → β → γ: penetration goes UP (paper → aluminium → lead) and ionising power goes DOWN (α strongest → γ weakest). Only γ (neutral) is not deflected by a field. To identify a radiation, use penetration to narrow it down, then deflection to confirm whether it is charged.
- Most penetrating ≠ most dangerous. From OUTSIDE the body alpha is safe (the skin stops it) but gamma is the bigger hazard; INSIDE the body (breathed in/swallowed) alpha is the most dangerous because of its strong ionising power.
- Every decay equation: the TOP numbers balance (nucleon number A conserved) and the BOTTOM numbers balance (proton number Z conserved). Alpha: A − 4, Z − 2. Beta-minus: A unchanged, Z + 1 — the electron's −1 charge forces Z UP, so never drop it.
- For a decay CHAIN, apply each emission one at a time and keep a running tally of A and Z. Use N = A − Z if asked for the neutron number.
- Energy released: find the mass defect FIRST (parent − total products), then E = mc². In MeV, just multiply Δm(in u) by 931.5. Keep every decimal place when subtracting masses — Δm is a tiny number and early rounding ruins it.
- Energy sharing: the parent is at rest, so the products have equal and opposite momentum; with KE = p²/2m the LIGHT product (alpha) carries most of the energy. Its share = mdₐᵤgₕₜₑᵣ ÷ (mdₐᵤgₕₜₑᵣ + mₐₗₚₕₐ), close to but just under 100% for a heavy parent.
- Half-life: ALWAYS subtract the background count rate before halving, then add it back if the question wants the measured value. Work out n = time ÷ half-life and multiply by (½)ⁿ — halve once per half-life, never subtract a fixed amount. Activity is in becquerel (Bq) = decays per second.
- Two samples with the SAME half-life keep the same RATIO of activities over time, because both fall by the same factor (½)ⁿ.