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
| Property | Alpha (α) | Beta-minus (β⁻) | Gamma (γ) |
|---|---|---|---|
| What it is | A helium nucleus (2 p + 2 n), ⁴₂He | A fast electron from the nucleus | A high-energy photon |
| Charge | +2 | −1 | 0 (neutral) |
| Penetration | Lowest — paper / a few cm of air / skin | Medium — a few mm of aluminium | Highest — thick lead or concrete |
| Ionising power | Strongest | Medium | Weakest |
| Deflected by a field? | Yes (small, +) | Yes (large, opposite way, −) | No (neutral) |
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
| Decay | What leaves the nucleus | Nucleon number A | Proton number Z |
|---|---|---|---|
| Alpha (α) | a helium-4 nucleus (2 p + 2 n) | falls by 4 (A → A − 4) | falls by 2 (Z → Z − 2) |
| Beta-minus (β⁻) | an electron + an antineutrino | unchanged (A → A) | rises by 1 (Z → Z + 1) |
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
| Half-life / activity | Energy released | |
|---|---|---|
| What it answers | How weak is the source after some time? | How much energy does one decay give out? |
| Key relationship | A = A₀ × (½)ⁿ, with n = time ÷ half-life | E = mc²; in MeV, Δm(u) × 931.5 |
| First step | Subtract the background count rate | Find the mass defect Δm = parent − total products |
| Units | Activity in becquerel (Bq) = decays per second | Energy in J or MeV (1 u = 931.5 MeV c⁻²) |
| Watch out for | HALVE each half-life — don't subtract a fixed amount | Keep ALL decimal places — Δm is a tiny number |
✏️ Worked exam-style questions
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.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
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.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
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.)
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
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.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
🧠 Quick self-check
Tap each card to reveal the answer.
Which radiation penetrates the FURTHEST, and which ionises the STRONGEST? Gamma (γ) penetrates furthest (needs thick lead); alpha (α) ionises the strongest (but is stopped by paper). Penetration and ionising power run in opposite orders.
In ALPHA decay, how do A and Z change? In BETA-MINUS? Alpha: A falls by 4, Z falls by 2. Beta-minus: A is unchanged, Z rises by 1 (a neutron becomes a proton, emitting an electron).
Why does the proton number RISE in beta-minus, not fall? The emitted electron has a bottom number of −1, so to keep the bottoms balanced the daughter's Z must be one MORE than the parent's. A neutron has turned into a proton.
Fast way to get the energy released in MeV from a mass defect? Find Δm in u (parent − total products), then multiply by 931.5 (since 1 u = 931.5 MeV c⁻²). The c² in E = mc² is already built into the 931.5.
Which decay product carries most of the energy, and why? The lighter one (the alpha). The parent is at rest, so the two products fly off with equal and opposite momentum; with KE = p²/2m, the smaller mass gets the bigger kinetic energy.
What must you do BEFORE halving a count rate over a half-life? Subtract the background count rate (true source rate = measured − background). Then halve the source rate once per half-life, and add the background back if the question wants the measured value.
🎯 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.