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Detailed notes on Atomic Physics for Cambridge IGCSE Coordinated Science, covering key concepts, explanations, examples, and exam-focused revision points.
Radioactive decay is the spontaneous emission of particles or waves from unstable nuclei. Cambridge tests alpha, beta, and gamma radiation properties, nuclear equations, half-life calculations, background radiation, and the uses and hazards of radioactivity.
Mapped to the Cambridge IGCSE 0654 syllabus (2025-2027).
Three types — know properties, penetration, deflection in fields, and how to distinguish them.
Alpha (α) radiation:
Beta (β) radiation:
Gamma (γ) radiation:
Comparison table:
| Property | Alpha (α) | Beta (β) | Gamma (γ) |
|---|---|---|---|
| Nature | He nucleus | Fast electron | EM wave |
| Charge | +2 | −1 | 0 |
| Ionising power | Highest | Medium | Lowest |
| Penetrating power | Lowest | Medium | Highest |
| Stopped by | Paper | Aluminium (5 mm) | Thick lead |
| Deflected by fields | Yes (positive) | Yes (negative) | No |
Write nuclear equations where mass number and atomic number are conserved on both sides.
Nuclear equation rules:
Alpha decay:
ᴬ_Z X → ᴬ⁻⁴_Z₋₂ Y + ⁴₂He
Example: Radium-226 alpha decay:
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He Check: A: 226 = 222 + 4 ✓; Z: 88 = 86 + 2 ✓
Beta decay:
ᴬ_Z X → ᴬ_Z₊₁ Y + ⁰₋₁e
Example: Carbon-14 beta decay:
¹⁴₆C → ¹⁴₇N + ⁰₋₁e Check: A: 14 = 14 + 0 ✓; Z: 6 = 7 + (−1) ✓
Gamma emission:
¹⁶⁶₇₇Ir* → ¹⁶⁶₇₇Ir + γ (asterisk = excited/energetic state)
Half-life is constant and independent of temperature, pressure, or chemical state.
Half-life (t½):
The time taken for half the radioactive nuclei in a sample to decay. OR: the time for the activity (count rate) to halve.
Properties of half-life:
Calculating remaining activity/nuclei:
| After n half-lives | Fraction remaining | Activity remaining |
|---|---|---|
| 0 | 1 (100%) | A₀ |
| 1 | ½ (50%) | ½A₀ |
| 2 | ¼ (25%) | ¼A₀ |
| 3 | ⅛ (12.5%) | ⅛A₀ |
| n | (½)ⁿ | (½)ⁿ × A₀ |
Example: Iodine-131 has t½ = 8 days. Initial activity = 1600 Bq. After 24 days (= 3 half-lives): Activity = 1600 × (½)³ = 1600/8 = 200 Bq.
Decay curves:
Background radiation:
Choosing a radioisotope for an application:
Hazards of radiation:
Nuclear fission (context):
Verbatim phrases and definitions Cambridge mark schemes credit.
Paper 4: 'Write the nuclear equation for the alpha decay of ²²⁶₈₈Ra' (2 marks — ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He). 'A radioactive source has initial activity 4800 Bq and half-life 6 hours. Calculate the activity after 18 hours' (3 marks — 18/6 = 3 half-lives; 4800 × (½)³ = 4800/8 = 600 Bq). 'State TWO properties of gamma radiation' (2 marks — electromagnetic wave; no charge; highly penetrating; stopped/reduced by thick lead; not deflected by fields; least ionising). 'Explain why a radioactive source for use as a medical tracer should have a short half-life' (2 marks — reduces radiation dose to patient; activity falls quickly → less harm after procedure).
Sources: Cambridge IGCSE Coordinated Sciences 0654 syllabus 2025-2027 (P8); 0654 Examiner Reports 2022-2024. Last reviewed 2026-05-14.
Step-by-step solutions to past-paper-style questions on radioactivity , written exactly the way a tutor would explain them at the board.
Question
Uranium-238 (92238U) undergoes alpha decay. Write the nuclear equation and identify the daughter nuclide.
Step-by-step solution
Step 1
An alpha particle is 24He. Atomic number decreases by 2; mass number decreases by 4.
92238U→ZAX+24He
Step 2
Conserve mass number: A=238−4=234.
A=234
Step 3
Conserve atomic number: Z=92−2=90 (thorium, Th).
92238U→90234Th+24He
Answer
92238U→90234Th+24α
Examiner tip
Check: top numbers (A): 234+4=238 ✓; bottom numbers (Z): 90+2=92 ✓. Always verify conservation.
Question
A radioactive source has an initial activity of 3200counts per minute. After 60minutes, the activity falls to 200counts per minute. Calculate the half-life of the source.
Step-by-step solution
Step 1
Find the number of half-lives elapsed.
2003200=16=24⟹4 half-lives
Step 2
Half-life = total time / number of half-lives.
t21=460=15minutes
Answer
Half-life =15minutes
Examiner tip
Count how many times the activity halves: 3200→1600→800→400→200 (4 halvings). Do not divide the ratio directly by 2.
Question
Compare alpha, beta, and gamma radiation in terms of (a) charge, (b) mass, (c) penetrating power, and (d) ionising ability. Explain the inverse relationship between penetrating power and ionising ability.
Step-by-step solution
Step 1
Alpha (α): charge +2, mass number 4 (helium nucleus). Stopped by a few centimetres of air or a sheet of paper. Strongly ionising.
Step 2
Beta (β−): charge −1, mass ≈1/1836 (fast electron). Stopped by a few mm of aluminium. Moderately ionising.
Step 3
Gamma (γ): charge 0, zero rest mass (EM wave). Reduced (not completely stopped) by several cm of lead or several metres of concrete. Weakly ionising.
Step 4
Inverse relationship: a strongly ionising particle loses energy rapidly as it ionises atoms. It is stopped quickly → short penetration. A weakly ionising radiation (gamma) rarely interacts with matter → retains energy over long distances → high penetration.
Answer
Alpha: +2 charge, A=4, stopped by paper, most ionising. Beta: −1, electron mass, stopped by Al, intermediate. Gamma: 0 charge, massless EM, requires Pb, least ionising. Strong ioniser → loses energy fast → short range.
Question
Carbon-14 (614C) undergoes beta-minus decay. Write the nuclear equation and identify the daughter nuclide.
Step-by-step solution
Step 1
In beta-minus decay, a neutron converts to a proton, emitting a beta particle (−10e or β−) and an antineutrino (ignored at IGCSE level).
Step 2
Mass number: unchanged (beta particle has negligible mass).
A=14
Step 3
Atomic number: increases by 1 (Z=6+1=7, nitrogen, N).
614C→714N+−10e
Answer
614C→714N+−10β
Examiner tip
Gamma emission does not change A or Z — the nucleus loses energy but no particles. Often accompanies alpha or beta decay.
The formulae you need to memorise for radioactivity on the Cambridge IGCSE 0654 paper, with every variable defined in plain English and a note on when to use it.
∑Areactants=∑Aproducts;∑Zreactants=∑Zproducts
When to use
Checking or completing any nuclear decay equation.
N=N0(21)n,n=t1/2t
When to use
Calculating remaining activity or nuclei after a given number of half-lives.
ZAX→Z−2A−4Y+24He
When to use
Writing an alpha decay equation.
ZAX→Z+1AY+−10e
When to use
Writing a beta-minus decay equation.
Definitions to memorise and the exact keywords mark schemes credit for radioactivity answers — sharpened from recent examiner reports for the 2026 0654 sitting.
A particle emitted in alpha decay consisting of 2 protons and 2 neutrons (a helium-4 nucleus). Charge +2; mass number 4. Strongly ionising; stopped by paper or a few cm of air.
A fast-moving electron emitted from the nucleus during beta-minus decay (a neutron converts to a proton). Charge −1; negligible mass. Moderately ionising; stopped by a few mm of aluminium.
High-energy electromagnetic radiation emitted from the nucleus. No charge; no mass. Weakly ionising; reduced (not completely stopped) by thick lead.
The time taken for half the radioactive nuclei in a sample to decay (or for the activity to fall to half its initial value). Half-life is constant for a given nuclide.
Low-level ionising radiation from natural and artificial sources that is always present in the environment. Sources: radon gas (largest natural source), cosmic rays, medical X-rays, nuclear industry. Must be subtracted from measured count rates in experiments.
Radioactive decay is random and spontaneous — it cannot be predicted when a particular nucleus will decay, and it is unaffected by temperature, pressure, chemical state, or any other external factor.
The traps other students keep falling into on radioactivity questions — taken from recent Cambridge IGCSE 0654 examiner reports and mark schemes — and how to avoid them.
Why it happens
Students know alpha is stopped by paper and generalise to 'safe'.
How to avoid it
Alpha is the most dangerous radiation when the source is inside the body (e.g., inhaled or ingested) — it is highly ionising and cannot escape. Externally, it is easily blocked. Context matters.
Why it happens
Students think 'half + half = all'.
How to avoid it
After 1 half-life: 50% remains. After 2: 25% remains. After 3: 12.5% remains. Each half-life halves the remaining amount — theoretically, some remains forever. In practice, after ~10 half-lives the amount is negligible.
Why it happens
Students apply only one conservation law.
How to avoid it
Always check both: mass numbers must balance AND atomic numbers must balance. Verify by adding both products' values and confirming they equal the parent's A and Z.
Why it happens
Students use the raw count rate without accounting for background.
How to avoid it
Corrected count rate = measured count rate − background count rate. Always state this step in practical/data questions.
The things students keep getting wrong in this sub-topic, answered.