Where can I learn Radioactive decay for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 23.2 (Radioactive decay) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/23-2-radioactive-decay.

Is Radioactive decay (23.2) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Radioactive decay.

How do I revise Radioactive decay for 9702 exams?

Start with the visual steps on this page, note the key exam points, then attempt a 9702 past-paper question on Radioactive decay using MarkScheme's /mark tool. Mark strictly against the official scheme and re-read any marks you lost.

MarkScheme 9702

Opening…

23.2Physics25 min readPREMIUM

Radioactive decay

Unstable atomic nuclei are constantly transforming into more stable configurations, a fundamental process known as radioactive decay. This fascinating phenomenon involves the emission of particles or electromagnetic radiation, shaping everything from medical treatments to determining the age of ancient artefacts. Let's delve into its core characteristics and how we quantify it. This pilot aligns with Senpai Corner A Level notes (2025-2027) for topic 23.2.

BY THE END, YOU CAN…

exam checklist — tick these off

1Describe the spontaneous and random nature of radioactive decay.
2Define and apply the terms decay constant, activity, and half-life.
3Use exponential decay equations and relationships to solve problems.
4Derive the relationship between half-life and decay constant.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Radioactive decay

Cambridge 9702 Paper 4 - Radioactive decay (23.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
23.2 Radioactive decay.
2
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
3
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
4
This proves that radioactive decay is both spontaneous and random .

What this topic covers

The official Cambridge syllabus points this lesson works through.

23.2.1
Understand that fluctuations in count rate provide evidence for the random nature of radioactive decay
23.2.2
Understand that radioactive decay is both spontaneous and random
23.2.3
Define activity and decay constant, and recall and use $A = λN$
23.2.4
Define half-life
23.2.5
Use $λ = 0.693/t_{1/2}$
23.2.6
Understand the exponential nature of radioactive decay, and sketch and use the relationship $x = x_0e^{-λt}$ , where x could represent activity, number of undecayed nuclei or received count rate

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Decay curve N falls exponentially: the more nuclei remain, the faster the count drops.

8 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

8 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 1Java · best on a laptop9702 23.2 · IB E.3
Alpha Decay
Watch a polonium-211 nucleus, or a custom one, emit an alpha particle; the timing chart shows when each decay happens.
Why this one: Watch a bucket of nuclei decay at random while the chart shows half of them gone after each half-life.
Try this
1. Reset and watch one nucleus — note how long it waits before decaying.
2. Reset again — the wait is different each time.
3. On the Multiple Nuclei screen, start 100 nuclei and read when half are gone.
Look for Decay is random for one nucleus but the half-life of a large sample is fixed.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhETStart here · 2Java · best on a laptop9702 23.2
Radioactive Dating Game
Measure how much carbon-14 or uranium-238 is left in rocks, bones and other objects and read off their age from the decay curve.
Why this one: Read how much carbon-14 remains and use the decay curve to find an object's age.
Try this
1. On the Half Life screen, start a batch of carbon-14 nuclei and read the time when half remain.
2. On the Dating Game screen, probe a bone with the carbon-14 detector — read the percentage left and slide the age until the curve matches.
3. Probe a rock with the uranium-238 detector instead — why is carbon-14 useless here?
Look for After n half-lives a fraction (½)ⁿ remains; choose an isotope whose half-life suits the age being measured.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhETStart here · 3Java · best on a laptop9702 23.2 · 11.1–11.2 · IB E.3
Beta Decay
Watch hydrogen-3 or carbon-14 nuclei undergo beta decay, emitting an electron and an antineutrino, with half-life timing.
Why this one: Watch carbon-14 nuclei decay one by one and compare the timing with the half-life.
Try this
1. Watch one hydrogen-3 nucleus decay — count the particles that leave.
2. Switch to carbon-14 — it waits much longer on average.
3. Start many nuclei and read the time when half have decayed.
Look for In β⁻ decay a neutron becomes a proton plus an electron and an antineutrino; Z rises by one.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 49702 23.2 · 9702 11.1 · IB E.3
Alpha Decay
Watch an alpha particle tunnel out of a heavy nucleus
Why this one: See what a single decay looks like: an alpha particle escaping a heavy nucleus.
Try this
1. Watch the alpha particle tunnel out of the nucleus.
2. Count the change in proton and nucleon numbers.
Look for The nucleus loses two protons and four nucleons.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
SimuPhysicsStart here · 59702 23.2 · IB E.3
Probability Simulator
Run coin tosses in bulk and watch the experimental fraction close in on the theoretical value
Why this one: Toss many coins and watch the fraction settle — random events, predictable in bulk.
Try this
1. Run 10 tosses and read the fraction.
2. Run 1000 and compare.
3. Run again and compare the two runs.
Look for The experimental fraction approaches the theoretical value as the number of trials grows.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations3 more on this topic — core ones first

3JCN PhysicsCore9702 23.2 · 9702 11.1 · IB E.3
Beta Decay
Watch a neutron become a proton with beta and antineutrino emission
Try this
1. Watch the neutron become a proton.
2. Identify the beta particle and the antineutrino.
Look for Nucleon number stays the same while proton number rises by one, with charge conserved.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 23.2 · 9702 11.1 · IB E.3
Gamma Decay
See an excited nucleus de-excite by emitting a gamma photon
Try this
1. Watch the excited nucleus emit the gamma photon.
2. Compare the nucleus before and after.
Look for Gamma emission changes neither proton nor nucleon number, only the energy of the nucleus.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 11.1 · 23.2 · IB E.4
Build a Nucleus
Add protons and neutrons to a nucleus and watch which decays it undergoes.
Try this
1. Build carbon-14 (6p, 8n) — the sim shows β⁻ decay; what does it become?
2. Build a heavy nucleus like uranium-238 — watch the α decay and the new Z and A.
3. On the “Chart”, trace a decay chain across the valley of stability.
Look for α: Z−2, A−4. β⁻: Z+1, A same. Too many neutrons → β⁻; too heavy → α.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$A = \lambda N$

Tap a symbol — great for exam definitions

KEY RELATION

$N = N_0 e^{-\lambda t}$

Tap a symbol — great for exam definitions

KEY RELATION

$t_{1/2} = \frac{\ln 2}{\lambda}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

The Nature of Radioactive Decay

Radioactive decay isn't something we can control or predict for a single nucleus. It possesses two crucial characteristics: it's spontaneous and random. This means it occurs without any external influence, such as changes in temperature or pressure, and we can't tell when a specific nucleus will decay. Evidence for this randomness comes from observing the count rate of a radioactive source with a Geiger-Muller tube; the readings fluctuate unpredictably around an average value, confirming that the decays are individual, random events.

23.2 Radioactive decay.
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
This proves that radioactive decay is both spontaneous and random .
The average decay rate (A) is the average number of nuclei which are expected to decay per unit overtime .
The decay constant is the probability that the nucleus will decay per unit time.

Not clear?

The Decay Constant (\lambda)

While individual decays are random, for a large sample, the overall rate of decay can be statistically predicted. The decay constant (symbol \lambda, pronounced 'lambda') helps us quantify this. It represents the probability that any single nucleus will decay per unit of time. A larger \lambda means a higher probability of decay and thus a less stable nucleus, leading to a shorter half-life. Conversely, a very small decay constant indicates a very stable isotope that decays slowly over a long period.

Definition: Probability of a single nucleus decaying per unit time.
Unit: Typically s^{-1} (per second) or year^{-1} (per year).
Higher \lambda means a shorter lifetime for the isotope.

Not clear?

Activity (A)

The activity of a radioactive sample measures how many nuclei are decaying per second. It's essentially the 'strength' of the radiation from a source. Since it's directly related to the decay constant and the number of undecayed nuclei, activity also decreases as the sample decays. While the SI unit is the Becquerel (Bq), an older, non-SI unit, the Curie (Ci), is sometimes encountered, where 1 Ci = 3.7 x 10¹⁰ Bq.

Activity, $A = \lambda N$ Where: $A$ = activity (Bq) $\lambda$ = decay constant (s^{-1}) $N$ = number of undecayed nuclei

Definition: The rate at which nuclei decay in a radioactive sample.
SI Unit: The Becquerel (Bq), where 1 Bq = 1 decay per second (s^{-1}).
Activity is directly proportional to the number of undecayed nuclei present.

Not clear?

Exponential Decay and Decay Curves

The number of undecayed nuclei, and consequently the activity, in a radioactive sample decreases exponentially over time. This means that in equal time intervals, the same fraction of remaining nuclei will decay, not the same absolute number. When plotted on a graph of N or A against time, this relationship produces a characteristic exponential decay curve that starts at N₀ (or A₀) and asymptotically approaches zero but never quite reaches it. These exponential relationships are critical for calculations.

Number of undecayed nuclei: $N = N_0 e^{-\lambda t}$ Activity: $A = A_0 e^{-\lambda t}$ Where: $N_0$ = initial number of nuclei $A_0$ = initial activity $N$ = number of nuclei at time $t$ $A$ = activity at time $t$ $e$ = Euler's number (approx. 2.718)

Not clear?

Half-Life ($t_{1/2}$)

The half-life is a unique characteristic for each radioactive isotope. It's the time it takes for exactly half of the radioactive nuclei in a sample to decay. After one half-life, 50% of the original sample remains. After two half-lives, 25% (half of 50%) remains, and so on. Importantly, the half-life remains constant, regardless of the initial amount of the substance or its physical conditions.

Half-life and decay constant: $t_{1/2} = \frac{\ln 2}{\lambda}$ Where: $t_{1/2}$ = half-life (s, min, hr, etc.) $\lambda$ = decay constant (s^{-1}, min^{-1}, hr^{-1}, etc.) $\ln 2 \approx 0.693$

Definition: Time for half of the nuclei in a sample to decay.
Constant: Unique for each isotope, independent of initial quantity.
After 'n' half-lives, the remaining fraction of nuclei (or activity) is $(1/2)^n$ .

Not clear?

Derivation of the Half-Life Formula

The relationship between half-life and the decay constant can be derived directly from the exponential decay equation. By definition, at the moment the time elapsed equals one half-life ( $t = t_{1/2}$ ), the number of remaining nuclei ( $N$ ) will be exactly half of the initial number ( $N = N_0 / 2$ ). By substituting these conditions into the decay equation, we can isolate and solve for $t_{1/2}$ .

Start with the decay equation: $N = N_0 e^{-\lambda t}$ Substitute $N = N_0/2$ and $t = t_{1/2}$ : $\frac{N_0}{2} = N_0 e^{-\lambda t_{1/2}}$ Divide by $N_0$ : $\frac{1}{2} = e^{-\lambda t_{1/2}}$ Take the natural logarithm (ln) of both sides: $\ln(\frac{1}{2}) = \ln(e^{-\lambda t_{1/2}})$ Using logarithm rules, $\ln(1/x) = -\ln(x)$ and $\ln(e^y) = y$ : $-\ln(2) = -\lambda t_{1/2}$ Finally, rearrange for $t_{1/2}$ : $t_{1/2} = \frac{\ln 2}{\lambda}$

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A radioactive isotope has a decay constant of $2.5 \times 10^{-3}$ s^{-1}. Calculate its half-life in seconds. Then, if a sample initially has an activity of 480 Bq, what will its activity be after 5.0 minutes?

1
Calculate the half-life ( $t_{1/2}$ ):

EXAMPLE 2

An ancient wooden artifact is found to have a carbon-14 activity of 0.180 Bq per gram of carbon. A modern, living sample of wood has an activity of 0.250 Bq per gram of carbon. Given that the half-life of carbon-14 is 5730 years, calculate the age of the artifact.

1
Calculate the decay constant (\lambda):

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEARadioactive decay

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

spontaneous: It possesses two crucial characteristics: it's spontaneous and random. This means it occurs without any external influence, such as changes in temperature or pressure, and we can't tell when a specific nucleus will decay.
decay constant: The decay constant (symbol \lambda, pronounced 'lambda') helps us quantify this.
activity: The activity of a radioactive sample measures how many nuclei are decaying per second. It's essentially the 'strength' of the radiation from a source.
half-life: The half-life is a unique characteristic for each radioactive isotope.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 10 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

23.2 Radioactive decay.
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
This proves that radioactive decay is both spontaneous and random .
The average decay rate (A) is the average number of nuclei which are expected to decay per unit overtime .
The decay constant is the probability that the nucleus will decay per unit time.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/22 · Q6(b)(ii)

PhysicsOctober/November 2024

(b) (ii)

State the names of the particles emitted as Q decays to form R.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/O/N/24

Question 2 of 29702/23 · Q6(b)(i)

PhysicsMay/June 2024

(b) (i)

This isotope of samarium is radioactive and decays by emitting particles. Gamma-radiation is not emitted. The energy spectrum of the emitted particles is shown in Fig. 6.1. Explain how Fig. 6.1 shows that this isotope of samarium emits α-particles and does not emit β-particles.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

Why is radioactive decay considered both spontaneous and random?

What is the practical significance of half-life in real-world applications?

Can radioactive decay be sped up or slowed down?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/22 · Q6(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS23.1 Mass defect and nuclear binding energy NEXT →24.1 Production and use of ultrasound

Discuss Radioactive decay

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Revise Radioactive decay for Cambridge 9702 (23.2)

Looking for free Physics 9702 notes on Radioactive decay? This A-Level lesson covers official syllabus point 23.2 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Radioactive decay 9702 revision", "9702 23.2 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

23.2Physics25 min readPREMIUM

Radioactive decay

BY THE END, YOU CAN…

exam checklist — tick these off

1Describe the spontaneous and random nature of radioactive decay.
2Define and apply the terms decay constant, activity, and half-life.
3Use exponential decay equations and relationships to solve problems.
4Derive the relationship between half-life and decay constant.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Radioactive decay

Cambridge 9702 Paper 4 - Radioactive decay (23.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
23.2 Radioactive decay.
2
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
3
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
4
This proves that radioactive decay is both spontaneous and random .

What this topic covers

The official Cambridge syllabus points this lesson works through.

23.2.1
Understand that fluctuations in count rate provide evidence for the random nature of radioactive decay
23.2.2
Understand that radioactive decay is both spontaneous and random
23.2.3
Define activity and decay constant, and recall and use $A = λN$
23.2.4
Define half-life
23.2.5
Use $λ = 0.693/t_{1/2}$
23.2.6
Understand the exponential nature of radioactive decay, and sketch and use the relationship $x = x_0e^{-λt}$ , where x could represent activity, number of undecayed nuclei or received count rate

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Decay curve N falls exponentially: the more nuclei remain, the faster the count drops.

8 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

8 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 1Java · best on a laptop9702 23.2 · IB E.3
Alpha Decay
Watch a polonium-211 nucleus, or a custom one, emit an alpha particle; the timing chart shows when each decay happens.
Why this one: Watch a bucket of nuclei decay at random while the chart shows half of them gone after each half-life.
Try this
1. Reset and watch one nucleus — note how long it waits before decaying.
2. Reset again — the wait is different each time.
3. On the Multiple Nuclei screen, start 100 nuclei and read when half are gone.
Look for Decay is random for one nucleus but the half-life of a large sample is fixed.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhETStart here · 2Java · best on a laptop9702 23.2
Radioactive Dating Game
Measure how much carbon-14 or uranium-238 is left in rocks, bones and other objects and read off their age from the decay curve.
Why this one: Read how much carbon-14 remains and use the decay curve to find an object's age.
Try this
1. On the Half Life screen, start a batch of carbon-14 nuclei and read the time when half remain.
2. On the Dating Game screen, probe a bone with the carbon-14 detector — read the percentage left and slide the age until the curve matches.
3. Probe a rock with the uranium-238 detector instead — why is carbon-14 useless here?
Look for After n half-lives a fraction (½)ⁿ remains; choose an isotope whose half-life suits the age being measured.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
PhETStart here · 3Java · best on a laptop9702 23.2 · 11.1–11.2 · IB E.3
Beta Decay
Watch hydrogen-3 or carbon-14 nuclei undergo beta decay, emitting an electron and an antineutrino, with half-life timing.
Why this one: Watch carbon-14 nuclei decay one by one and compare the timing with the half-life.
Try this
1. Watch one hydrogen-3 nucleus decay — count the particles that leave.
2. Switch to carbon-14 — it waits much longer on average.
3. Start many nuclei and read the time when half have decayed.
Look for In β⁻ decay a neutron becomes a proton plus an electron and an antineutrino; Z rises by one.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 49702 23.2 · 9702 11.1 · IB E.3
Alpha Decay
Watch an alpha particle tunnel out of a heavy nucleus
Why this one: See what a single decay looks like: an alpha particle escaping a heavy nucleus.
Try this
1. Watch the alpha particle tunnel out of the nucleus.
2. Count the change in proton and nucleon numbers.
Look for The nucleus loses two protons and four nucleons.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
SimuPhysicsStart here · 59702 23.2 · IB E.3
Probability Simulator
Run coin tosses in bulk and watch the experimental fraction close in on the theoretical value
Why this one: Toss many coins and watch the fraction settle — random events, predictable in bulk.
Try this
1. Run 10 tosses and read the fraction.
2. Run 1000 and compare.
3. Run again and compare the two runs.
Look for The experimental fraction approaches the theoretical value as the number of trials grows.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations3 more on this topic — core ones first

3JCN PhysicsCore9702 23.2 · 9702 11.1 · IB E.3
Beta Decay
Watch a neutron become a proton with beta and antineutrino emission
Try this
1. Watch the neutron become a proton.
2. Identify the beta particle and the antineutrino.
Look for Nucleon number stays the same while proton number rises by one, with charge conserved.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 23.2 · 9702 11.1 · IB E.3
Gamma Decay
See an excited nucleus de-excite by emitting a gamma photon
Try this
1. Watch the excited nucleus emit the gamma photon.
2. Compare the nucleus before and after.
Look for Gamma emission changes neither proton nor nucleon number, only the energy of the nucleus.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 11.1 · 23.2 · IB E.4
Build a Nucleus
Add protons and neutrons to a nucleus and watch which decays it undergoes.
Try this
1. Build carbon-14 (6p, 8n) — the sim shows β⁻ decay; what does it become?
2. Build a heavy nucleus like uranium-238 — watch the α decay and the new Z and A.
3. On the “Chart”, trace a decay chain across the valley of stability.
Look for α: Z−2, A−4. β⁻: Z+1, A same. Too many neutrons → β⁻; too heavy → α.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$A = \lambda N$

Tap a symbol — great for exam definitions

KEY RELATION

$N = N_0 e^{-\lambda t}$

Tap a symbol — great for exam definitions

KEY RELATION

$t_{1/2} = \frac{\ln 2}{\lambda}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

The Nature of Radioactive Decay

23.2 Radioactive decay.
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
This proves that radioactive decay is both spontaneous and random .
The average decay rate (A) is the average number of nuclei which are expected to decay per unit overtime .
The decay constant is the probability that the nucleus will decay per unit time.

Not clear?

The Decay Constant (\lambda)

Definition: Probability of a single nucleus decaying per unit time.
Unit: Typically s^{-1} (per second) or year^{-1} (per year).
Higher \lambda means a shorter lifetime for the isotope.

Not clear?

Activity (A)

Activity, $A = \lambda N$ Where: $A$ = activity (Bq) $\lambda$ = decay constant (s^{-1}) $N$ = number of undecayed nuclei

Definition: The rate at which nuclei decay in a radioactive sample.
SI Unit: The Becquerel (Bq), where 1 Bq = 1 decay per second (s^{-1}).
Activity is directly proportional to the number of undecayed nuclei present.

Not clear?

Exponential Decay and Decay Curves

Not clear?

Half-Life ($t_{1/2}$)

Half-life and decay constant: $t_{1/2} = \frac{\ln 2}{\lambda}$ Where: $t_{1/2}$ = half-life (s, min, hr, etc.) $\lambda$ = decay constant (s^{-1}, min^{-1}, hr^{-1}, etc.) $\ln 2 \approx 0.693$

Definition: Time for half of the nuclei in a sample to decay.
Constant: Unique for each isotope, independent of initial quantity.
After 'n' half-lives, the remaining fraction of nuclei (or activity) is $(1/2)^n$ .

Not clear?

Derivation of the Half-Life Formula

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

1
Calculate the half-life ( $t_{1/2}$ ):

EXAMPLE 2

1
Calculate the decay constant (\lambda):

How it all connects

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MAIN IDEARadioactive decay

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Glossary

Key terms for this topic — skim now; the Check step will test them.

spontaneous: It possesses two crucial characteristics: it's spontaneous and random. This means it occurs without any external influence, such as changes in temperature or pressure, and we can't tell when a specific nucleus will decay.
decay constant: The decay constant (symbol \lambda, pronounced 'lambda') helps us quantify this.
activity: The activity of a radioactive sample measures how many nuclei are decaying per second. It's essentially the 'strength' of the radiation from a source.
half-life: The half-life is a unique characteristic for each radioactive isotope.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

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Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

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Your guess — write it before you look

1 / 10 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

23.2 Radioactive decay.
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particles .
Evidence for the random nature of radioactive decay can be seen from the fluctuations in the count rate of a Geiger-Muller counter.
This proves that radioactive decay is both spontaneous and random .
The average decay rate (A) is the average number of nuclei which are expected to decay per unit overtime .
The decay constant is the probability that the nucleus will decay per unit time.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/22 · Q6(b)(ii)

PhysicsOctober/November 2024

(b) (ii)

State the names of the particles emitted as Q decays to form R.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/O/N/24

Question 2 of 29702/23 · Q6(b)(i)

PhysicsMay/June 2024

(b) (i)

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Extra simulations & links

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Frequently asked

Why is radioactive decay considered both spontaneous and random?

What is the practical significance of half-life in real-world applications?

Can radioactive decay be sped up or slowed down?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/22 · Q6(b)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

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Revise Radioactive decay for Cambridge 9702 (23.2)

In simple terms

What this topic covers

Explore the concept

Simulations

Alpha Decay

Radioactive Dating Game

Beta Decay

Alpha Decay

Probability Simulator

Beta Decay

Gamma Decay

Build a Nucleus

Key formulas

Full topic notes

The Nature of Radioactive Decay

The Decay Constant (\lambda)

Activity (A)

Exponential Decay and Decay Curves

Half-Life ($t_{1/2}$)

Derivation of the Half-Life Formula

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Radioactive decay

Revise Radioactive decay for Cambridge 9702 (23.2)

In simple terms

What this topic covers

Explore the concept

Simulations

Alpha Decay

Radioactive Dating Game

Beta Decay

Alpha Decay

Probability Simulator

Beta Decay

Gamma Decay

Build a Nucleus

Key formulas

Full topic notes

The Nature of Radioactive Decay

The Decay Constant (\lambda)

Activity (A)

Exponential Decay and Decay Curves

Half-Life ($t_{1/2}$)

Derivation of the Half-Life Formula

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Radioactive decay