Random decay, radiation, activity and half-life
Key idea: A reviewed, static H2 Physics learning chain for all official Nuclear Physics outcomes, from Rutherford evidence to fusion and fission.
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The core idea
Build the idea
Learn the idea
Big question: How can random individual decays produce a predictable population law?
Each unstable nucleus decays spontaneously and randomly with constant probability per unit time. For a large sample, N = N₀e⁻λt and activity A = λN, with half-life t½ = ln2/λ. Alpha, beta and gamma radiation differ in charge, ionising power, penetration and behaviour in fields.
Separate unpredictable events from a predictable population
Nuclear decay is spontaneous and random: no external trigger is required, and the decay time of one nucleus cannot be predicted. Repeated counts fluctuate even when the average activity is steady.
Background radiation comes from sources such as cosmic rays, rocks and building materials. Measure it separately and subtract its mean count rate before inferring source behaviour.
Check your understanding: Do fluctuating counts prove the source activity is changing?
No. Random fluctuations are expected; look for a sustained change beyond the scatter.
Connect decay constant, activity and the exponential
The decay constant λ is the probability per unit time that one nucleus decays. For a large population, N = N₀e⁻λt and activity A = λN, so activity follows the same exponential form.
Half-life satisfies t½ = ln2/λ. Equal half-life intervals multiply N or A by one half; they do not subtract equal amounts. Activity is measured in becquerels, where 1 Bq means one decay per second.
Check your understanding: What fraction remains after three half-lives?
(1/2)³ = 1/8.
Distinguish alpha, beta and gamma radiation
Alpha radiation is a helium nucleus with charge +2e, beta-minus is a fast electron with charge −e and gamma is an electromagnetic photon with no charge. Alpha is strongly ionising and weakly penetrating; gamma is less densely ionising and highly penetrating; beta is intermediate.
Electric and magnetic fields deflect charged alpha and beta emissions in opposite directions, with beta normally curving more because of its much smaller mass. Gamma is not deflected.
Check your understanding: Which emission is undeflected by an electric field and why?
Gamma, because it has no electric charge.
Key ideas to keep
- Activity is measured in becquerels; a measured count rate may include background and is not automatically the source activity.
- Half-life is independent of the initial number in the ideal model.
- Random decay does not mean the population curve is unpredictable.
See the reasoning
Worked example
Move from activity data to half-life, decay constant and nuclei
Question: A sample's activity falls from 800 Bq to 200 Bq in 600 s. Find its half-life, decay constant and initial number of undecayed nuclei.
Step 1: Count the halvings
Why: 800 to 200 is a factor of four.
Working: Two half-lives occur in 600 s, so t½ = 300 s.
Step 2: Find the decay constant
Why: Half-life and decay constant describe the same exponential.
Working: λ = ln2/300 = 2.31 × 10⁻³ s⁻¹.
Step 3: Use activity as decay rate
Why: A = λN links the macroscopic activity to population size.
Working: N₀ = 800/(2.31×10⁻³) = 3.46 × 10⁵ nuclei.
Answer: t½ = 300 s, λ = 2.31 × 10⁻³ s⁻¹ and N₀ = 3.46 × 10⁵ nuclei.
Check: A smaller λ would require more nuclei to produce the same activity, which matches A = λN.
Another worked model
Question
Net activity falls from 960 to 240 Bq in 12 min. Find half-life and λ.
Check the worked solution
Two halvings occur, so t½ = 6 min = 360 s and λ = ln2/360 = 1.93 × 10⁻³ s⁻¹.
Use a hint if needed
Practise with support
Try this
Three half-lives pass. State the remaining fraction.
Hint: Apply one factor 1/2 per half-life.
Check your answer
1/8.
Now work without the hint
Practise independently
Your turn
Explain randomness, count fluctuations, background, radiation properties and the equations A = λN and x = x₀e⁻λt.
Check your answer
Individual decay time is unpredictable but population probability is constant. Counts fluctuate statistically and include environmental background. Alpha, beta and gamma differ in nature, ionisation and penetration. λ links activity to undecayed nuclei; exponential decay gives t½ = ln2/λ.
Avoid these traps
Common mistakes
Common mistake
Half-life predicts when one nucleus decays.
What is wrong with this reasoning?
Show better thinking
It describes a population; individual decay is random.
Common mistake
Measured count rate is automatically source activity.
What is wrong with this reasoning?
Show better thinking
Subtract background and account for detection efficiency before inference.
Write for the examiner
Exam guidance
Subtract background count rate before using measurements and retain the exponential, rather than subtracting equal amounts each half-life.
Exam-style practice [7 marks]
A detector records 920 counts min⁻¹ initially and 150 counts min⁻¹ after 30 min. Background is 40 counts min⁻¹. Find the half-life and decay constant. The initial source activity is 58.0 Bq; estimate the initial number of undecayed nuclei.
Plan before you answer
- Subtract background from both count rates.
- Use the corrected ratio to count halvings.
- Use the stated activity in A = λN.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
Corrected rates are 920 − 40 = 880 and 150 − 40 = 110 counts min⁻¹. The factor 880/110 = 8 represents three half-lives in 30 min, so t½ = 10 min = 600 s and λ = ln2/600 = 1.16 × 10⁻³ s⁻¹. From A = λN, N = 58.0/(1.16×10⁻³) ≈ 5.0 × 10⁴ nuclei.
Exam-style practice [6 marks]
Compare alpha, beta-minus and gamma radiation by nature, charge, ionising effect and penetration. State how each behaves in an electric field.
Plan before you answer
- Identify what each radiation consists of.
- Connect charge to field deflection.
- Compare ionisation and penetration oppositely.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
Alpha is a helium nucleus with charge +2e, is strongly ionising and weakly penetrating, and deflects towards the negative plate. Beta-minus is an electron with charge −e, has intermediate penetration and ionisation, and deflects oppositely and more strongly. Gamma is an uncharged electromagnetic photon, is highly penetrating and less densely ionising, and is not deflected.
Come back in three days
Check what stayed with you
Recall question 1
Define decay constant.
Check the answer
The probability per unit time that one undecayed nucleus decays.
Recall question 2
State the activity relation.
Check the answer
A = λN.
Recall question 3
Why subtract background count rate?
Check the answer
It is not caused by the source and would distort activity and half-life inferences.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 20 excludes knowledge of positron emission in 20(g) and detailed knowledge of the antineutrino and particle zoo in 20(o). Nuclide equations conserve nucleon number, charge, mass-energy and momentum. Count data require background correction before population-law inference. Applications must relate half-life, penetration and ionisation to benefit and hazard. The binding-energy-per-nucleon curve, not a claim that mass disappears, explains fusion and fission energy release.
- GCE A-Level H2 PhysicsTopic 20(d) / Topic 20(e) / Topic 20(f) / Topic 20(g) / Topic 20(h) / Topic 20(i) / Topic 20(j) / Topic 20(k) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027