What is radioactivity and how is it related to atomic physics in the Cambridge IGCSE Coordinated Science curriculum?

Radioactivity is the process by which unstable atomic nuclei lose energy by emitting radiation. In the Cambridge IGCSE Coordinated Science curriculum, it is studied under Atomic Physics, where students learn about the types of radiation, their properties, and their effects on matter.

What are the three main types of radioactive decay covered in the Cambridge IGCSE Coordinated Science syllabus?

The three main types of radioactive decay are alpha decay, beta decay, and gamma decay. Alpha decay involves the emission of an alpha particle, beta decay involves the emission of a beta particle, and gamma decay involves the emission of gamma rays. Each type has distinct properties and effects, which are important topics in the Cambridge IGCSE Coordinated Science syllabus.

How do you differentiate between alpha, beta, and gamma radiation in terms of their properties and penetration power?

Alpha particles are heavy and positively charged, with low penetration power, stopped by paper or skin. Beta particles are lighter, negatively charged, and have moderate penetration power, stopped by aluminum. Gamma rays are electromagnetic waves with no charge and high penetration power, requiring thick lead or concrete for shielding. Understanding these differences is crucial in the study of radioactivity in Atomic Physics.

What is half-life and why is it significant in the study of radioactivity in the Cambridge IGCSE curriculum?

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is significant because it helps determine the rate of decay and the stability of a radioactive isotope. In the Cambridge IGCSE curriculum, students learn to calculate and interpret half-life to understand radioactive processes and their applications.

What are some practical applications of radioactivity that students learn about in the Cambridge IGCSE Coordinated Science course?

Students learn about various applications of radioactivity, including medical uses like cancer treatment with radiation therapy, industrial applications such as radiography for inspecting welds, and scientific uses like carbon dating for determining the age of archaeological finds. These applications highlight the importance of radioactivity in different fields.

Why is "Saying alpha particles are 'harmless' because they are easily stopped" a common mistake in Radioactivity ?

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 is "Saying 'after two half-lives, all the radioactive material has decayed'" a common mistake in Radioactivity ?

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 is "Changing $Z$ but not $A$ in alpha decay (or vice versa)" a common mistake in Radioactivity ?

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 is "Not subtracting background radiation from measured count rates" a common mistake in Radioactivity ?

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.

Cambridge IGCSE Coordinated Science (0654)

Radioactivity

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Short Notes - Radioactivity

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Detailed Study Notes

Detailed notes on Atomic Physics for Cambridge IGCSE Coordinated Science, covering key concepts, explanations, examples, and exam-focused revision points.

Radioactivity — Cambridge IGCSE Coordinated Science 0654

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.

At a glance

Alpha (α): helium nucleus (²He₄). Stopped by paper/skin. Highly ionising. Short range in air.
Beta (β): fast electron. Stopped by 5–10 mm aluminium. Moderately ionising.
Gamma (γ): electromagnetic wave. Reduced (not stopped) by thick lead. Least ionising, most penetrating.
Half-life: time for half the radioactive nuclei in a sample to decay. Constant; independent of conditions.
Nuclear equations: mass number and atomic number must balance on both sides.

What you’ll learn

Mapped to the Cambridge IGCSE 0654 syllabus (2025-2027).

P8.2a — Describe alpha, beta, and gamma radiation properties, ionising power, and penetrating power.
P8.2b — Write nuclear equations for alpha and beta decay.
P8.2c — Define half-life and use it in calculations.
P8.2d — Describe background radiation, uses, and hazards of radioactivity.

Types of Nuclear Radiation

Three types — know properties, penetration, deflection in fields, and how to distinguish them.

Alpha (α) radiation:

Nature: helium nucleus; 2 protons + 2 neutrons → ⁴₂He
Charge: +2
Mass: 4 (relative)
Ionising power: highest (large charge → easily knocks electrons off atoms)
Penetrating power: lowest — stopped by a few cm of air or a sheet of paper
Deflected by electric and magnetic fields (positive charge → deflects away from positive plate)
Nuclide change: atomic number decreases by 2; mass number decreases by 4

Beta (β) radiation:

Nature: fast-moving electron emitted from nucleus (neutron → proton + electron + antineutrino)
Charge: −1
Mass: negligible
Ionising power: moderate
Penetrating power: moderate — stopped by ~5 mm of aluminium
Deflected by electric and magnetic fields (negative → opposite direction to alpha)
Nuclide change: atomic number increases by 1; mass number unchanged

Gamma (γ) radiation:

Nature: high-energy electromagnetic wave (photon)
Charge: 0
Mass: 0
Ionising power: lowest
Penetrating power: highest — reduced (but not fully stopped) by several cm of dense lead
Not deflected by electric or magnetic fields (no charge)
Nuclide change: none (nucleus loses energy only; Z and A unchanged)

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

α (+2) bends slightly to the negative plate, β⁻ (−1) bends strongly to the positive plate, γ passes straight through.

Alpha: ⁴₂He; most ionising, least penetrating; stopped by paper.
Beta: electron; moderate ionising and penetrating; stopped by aluminium.
Gamma: EM wave; least ionising, most penetrating; lead reduces it.

Nuclear Equations

Write nuclear equations where mass number and atomic number are conserved on both sides.

Nuclear equation rules:

Total mass number (A) must balance on both sides
Total atomic number (Z) must balance on both sides

Alpha decay:

ᴬ_Z X → ᴬ⁻⁴_Z₋₂ Y + ⁴₂He

Mass number decreases by 4
Atomic number decreases by 2

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

Mass number unchanged
Atomic number increases by 1
A neutron in the nucleus converts to a proton + emitted electron (beta particle)

Example: Carbon-14 beta decay:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e Check: A: 14 = 14 + 0 ✓; Z: 6 = 7 + (−1) ✓

Gamma emission:

No change to A or Z (nucleus just loses energy)
Often accompanies alpha or beta decay

¹⁶⁶₇₇Ir* → ¹⁶⁶₇₇Ir + γ (asterisk = excited/energetic state)

Nuclear equations: A and Z must balance on each side.
Alpha decay: A −4, Z −2. Beta decay: A unchanged, Z +1.
Gamma: no change to A or Z.

Half-Life and Radioactive Decay

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:

Constant for a given isotope (unaffected by temperature, pressure, chemical environment)
Radioactive decay is random — cannot predict when any single nucleus will decay
But with large numbers, statistical behaviour is very predictable

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:

Graph of activity vs time: decreasing exponential curve
Count rate starts high, decreases and asymptotically approaches background

Background radiation:

Low-level ionising radiation always present in the environment
Sources: cosmic rays, radon gas (from rocks/soil), medical procedures, food, building materials
Must subtract background count from measured count rate: corrected count = measured − background

Choosing a radioisotope for an application:

Half-life: short enough for radiation to decay quickly when harmful (e.g., medicine); long enough to still be active when needed
Type of radiation: depends on application
- Smoke detectors: americium-241 (α) — ionises air, detected by circuit; long t½ (432 years)
- Medical tracers: technetium-99m (γ) — penetrates body for imaging; short t½ (6 hours)
- Sterilisation: gamma (penetrates packaging, kills bacteria)
- Thickness gauges: beta (appropriate penetration)
- Radiotherapy: gamma (kills cancer cells)

Hazards of radiation:

Ionising radiation damages DNA → cancer, mutations
Alpha: most dangerous if inhaled/ingested (most ionising); least dangerous externally
External: gamma and beta most dangerous (penetrate skin)
Precautions: minimise exposure time, maximise distance, use shielding (lead aprons), handle with tongs, no eating near sources

Nuclear fission (context):

Heavy nucleus (e.g., U-235) absorbs a neutron → splits into two smaller nuclei + 2–3 neutrons + energy
Chain reaction: released neutrons cause further fissions
Controlled in nuclear reactor → produces heat → electricity

Half-life: time for activity to halve. Constant; independent of conditions.
After n half-lives: fraction remaining = (½)ⁿ.
Background radiation: always present; subtract from measurements.

Quick recap

Alpha: He nucleus; most ionising; paper stops it. Beta: electron; aluminium. Gamma: EM wave; lead.
Nuclear equations: A and Z balance. Alpha: A−4, Z−2. Beta: A same, Z+1.
Half-life: constant; activity halves each t½. After n t½: (½)ⁿ of original.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Alpha decay — A decreases by 4; Z decreases by 2; emits ⁴₂He.
Beta decay — A unchanged; Z increases by 1; emits ⁰₋₁e.
Half-life — constant; time for activity to halve; unaffected by temperature/pressure.
Alpha: most ionising, least penetrating. Gamma: least ionising, most penetrating.
Background radiation — always present; must subtract from measurements.

How it’s examined

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.

Take this whole topic with you

Step-by-step worked examples — Radioactivity

Step-by-step solutions to past-paper-style questions on radioactivity , written exactly the way a tutor would explain them at the board.

1Writing a nuclear decay equation for alpha emission
Core• alpha decay, nuclear equation, conservation
Question
Uranium-238 ( $^{238}_{92}\text{U}$ ) undergoes alpha decay. Write the nuclear equation and identify the daughter nuclide.
Step-by-step solution
1. Step 1
  An alpha particle is $^{4}_{2}\text{He}$ . Atomic number decreases by 2; mass number decreases by 4.
  $^{238}_{92}\text{U} \rightarrow ^{A}_{Z}\text{X} + ^{4}_{2}\text{He}$
2. Step 2
  Conserve mass number: $A = 238 - 4 = 234$ .
  $A = 234$
3. Step 3
  Conserve atomic number: $Z = 92 - 2 = 90$ (thorium, Th).
  $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$
Answer
$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\alpha$
Examiner tip
Check: top numbers ( $A$ ): $234 + 4 = 238$ ✓; bottom numbers ( $Z$ ): $90 + 2 = 92$ ✓. Always verify conservation.
2Half-life calculation
Extended• Adapted from 0654/42 May/Jun 2024 Q8• half-life, activity, radioactive decay
Question
A radioactive source has an initial activity of $3200\,\text{counts per minute}$ . After $60\,\text{minutes}$ , the activity falls to $200\,\text{counts per minute}$ . Calculate the half-life of the source.
Step-by-step solution
1. Step 1
  Find the number of half-lives elapsed.
  $\dfrac{3200}{200} = 16 = 2^{4} \implies 4 \text{ half-lives}$
2. Step 2
  Half-life $=$ total time / number of half-lives.
  $t_{\frac{1}{2}} = \dfrac{60}{4} = 15\,\text{minutes}$
Answer
Half-life $= 15\,\text{minutes}$
Examiner tip
Count how many times the activity halves: $3200 \to 1600 \to 800 \to 400 \to 200$ (4 halvings). Do not divide the ratio directly by 2.
3Comparing properties of alpha, beta, and gamma radiation
Challenge• alpha, beta, gamma, penetration, ionisation
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
1. Step 1
  Alpha ( $\alpha$ ): charge $+2$ , mass number $4$ (helium nucleus). Stopped by a few centimetres of air or a sheet of paper. Strongly ionising.
2. Step 2
  Beta ( $\beta^{-}$ ): charge $-1$ , mass $\approx 1/1836$ (fast electron). Stopped by a few mm of aluminium. Moderately ionising.
3. Step 3
  Gamma ( $\gamma$ ): charge $0$ , zero rest mass (EM wave). Reduced (not completely stopped) by several cm of lead or several metres of concrete. Weakly ionising.
4. 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.
4Beta-minus decay equation
Extended• beta decay, nuclear equation, neutron to proton
Question
Carbon-14 ( $^{14}_{6}\text{C}$ ) undergoes beta-minus decay. Write the nuclear equation and identify the daughter nuclide.
Step-by-step solution
1. Step 1
  In beta-minus decay, a neutron converts to a proton, emitting a beta particle ( $^{0}_{-1}\text{e}$ or $\beta^{-}$ ) and an antineutrino (ignored at IGCSE level).
2. Step 2
  Mass number: unchanged (beta particle has negligible mass).
  $A = 14$
3. Step 3
  Atomic number: increases by 1 ( $Z = 6 + 1 = 7$ , nitrogen, N).
  $^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}$
Answer
$^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\beta$
Examiner tip
Gamma emission does not change $A$ or $Z$ — the nucleus loses energy but no particles. Often accompanies alpha or beta decay.

Key Formulae — Radioactivity

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.

Conservation in nuclear equations
$\sum A_{\text{reactants}} = \sum A_{\text{products}}; \quad \sum Z_{\text{reactants}} = \sum Z_{\text{products}}$
$A$
mass number
$Z$
atomic number (charge number)
When to use
Checking or completing any nuclear decay equation.
Half-life
$N = N_0 \left(\dfrac{1}{2}\right)^{n}, \quad n = \dfrac{t}{t_{1/2}}$
$N$
number of undecayed nuclei at time $t$
$N_0$
initial number of undecayed nuclei
$n$
number of half-lives elapsed
$t_{1/2}$
half-life (s, min, hours, etc.)
When to use
Calculating remaining activity or nuclei after a given number of half-lives.
Alpha decay
$^{A}_{Z}\text{X} \rightarrow ^{A-4}_{Z-2}\text{Y} + ^{4}_{2}\text{He}$
$\text{X}$
parent nuclide
$\text{Y}$
daughter nuclide
When to use
Writing an alpha decay equation.
Beta-minus decay
$^{A}_{Z}\text{X} \rightarrow ^{A}_{Z+1}\text{Y} + ^{0}_{-1}\text{e}$
$\text{X}$
parent nuclide
$\text{Y}$
daughter nuclide
When to use
Writing a beta-minus decay equation.

Key Definitions and Keywords — Radioactivity

Definitions to memorise and the exact keywords mark schemes credit for radioactivity answers — sharpened from recent examiner reports for the 2026 0654 sitting.

Alpha particle ( $\alpha$ )
Examiner keyword
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.
Beta particle ( $\beta^{-}$ )
Examiner keyword
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.
Gamma radiation ( $\gamma$ )
Examiner keyword
High-energy electromagnetic radiation emitted from the nucleus. No charge; no mass. Weakly ionising; reduced (not completely stopped) by thick lead.
Half-life
Examiner keyword
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.
Background radiation
Examiner keyword
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.
Spontaneous decay
Examiner keyword
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.

Common Mistakes and Misconceptions — Radioactivity

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.

✕Saying alpha particles are 'harmless' because they are easily stopped
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.
✕Saying 'after two half-lives, all the radioactive material has decayed'
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.
✕Changing $Z$ but not $A$ in alpha decay (or vice versa)
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 $Z$ .
✕Not subtracting background radiation from measured count rates
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.

Radioactivity — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Radioactivity

Short Notes - Radioactivity

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Writing a nuclear decay equation for alpha emission

2Half-life calculation

3Comparing properties of alpha, beta, and gamma radiation

4Beta-minus decay equation

Conservation in nuclear equations

Half-life

Alpha decay

Beta-minus decay

Alpha particle (α\alphaα)

Beta particle (β−\beta^{-}β−)

Gamma radiation (γ\gammaγ)

Half-life

Background radiation

Spontaneous decay

✕Saying alpha particles are 'harmless' because they are easily stopped

✕Saying 'after two half-lives, all the radioactive material has decayed'

✕Changing ZZZ but not AAA in alpha decay (or vice versa)

✕Not subtracting background radiation from measured count rates

Radioactivity — frequently asked questions

Alpha particle ( $\alpha$ )

Beta particle ( $\beta^{-}$ )

Gamma radiation ( $\gamma$ )

✕Changing $Z$ but not $A$ in alpha decay (or vice versa)