Describe radioactive decay and relate activity to nuclei
Use count-rate fluctuations as evidence of random decay, and relate activity to the number of undecayed nuclei.
Section 23 · Nuclear physics
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. The Topic 23 outcomes were also checked against Cambridge’s 2028–2030 syllabus, which reports no significant teaching changes. Online practice is self-checked and cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use scientific notation, SI units, proportional reasoning and the particle numbers in nuclide notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does one becquerel represent?
What you will learn
- Interpret count-rate fluctuations as evidence of random radioactive decay
- Define spontaneous and random decay
- Define activity and decay constant and use A = λN
Radioactive decay is spontaneous and random
Spontaneous decay occurs without an external trigger deciding when a particular nucleus decays. Random decay means it is not possible to predict which individual nucleus will decay next or the exact time it will decay.
A large sample can show a predictable average trend even though individual events are random. Fluctuations in count rate over equal time intervals provide evidence of that random nature.
Activity counts decays per unit time
Activity A is the number of nuclear decays per unit time. One becquerel (Bq) is one decay per second. The decay constant λ is the probability per unit time that a nucleus decays; its unit is the reciprocal of the chosen time unit.
The relation A = λN connects activity with the number N of undecayed nuclei. Keep the time units compatible: if λ is in s⁻¹, A is in Bq when N is a count of nuclei.
Pause and explain
A sample has N = 5.0 × 10⁵ and λ = 2.0 × 10⁻³ s⁻¹. What is A?
Worked example
A sample contains 2.0 × 10⁶ undecayed nuclei and has decay constant 3.0 × 10⁻⁴ s⁻¹. Find its activity.
Show the worked solution
- Use A = λN.
- A = 3.0 × 10⁻⁴ × 2.0 × 10⁶.
- The seconds cancel to give decays per second.
Answer A = 6.0 × 10² Bq
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A radioactive sample has N = 8.0 × 10⁷ nuclei and λ = 4.0 × 10⁻⁵ s⁻¹. Calculate activity.
Give me a hint
Multiply the decay constant by the number of undecayed nuclei.
Compare my reasoning
- A = λN.
- A = 4.0 × 10⁻⁵ × 8.0 × 10⁷.
- A = 32 × 10² = 3.2 × 10³ s⁻¹.
3.2 × 10³ Bq.
Look for these in your work
- Uses A = λN
- Multiplies the coefficients
- Converts to Bq
Explain what repeated fluctuations in equal-duration count measurements tell you about radioactive decay.
Give me a hint
Separate the behaviour of individual events from the average behaviour of a large sample.
Compare my reasoning
- Counts differ from one equal interval to another.
- The differences are not evidence that each nucleus follows a predictable schedule.
- They support the conclusion that decay events are random.
The fluctuating count rate is evidence that individual radioactive decays are random.
Look for these in your work
- Notes equal time intervals
- Identifies variation in counts
- Connects fluctuations with randomness
A measured decay constant is 0.12 min⁻¹ and there are 2.5 × 10⁴ undecayed nuclei. Find activity in decays per minute.
Give me a hint
Keep the time unit as minutes for both λ and the activity result.
Compare my reasoning
- A = λN = 0.12 × 2.5 × 10⁴ per minute.
- 0.12 × 2.5 = 0.30.
- A = 0.30 × 10⁴ = 3.0 × 10³ decays per minute.
3.0 × 10³ decays per minute (not Bq).
Look for these in your work
- Uses consistent minutes
- Calculates λN
- Does not label per-minute activity as Bq
Common mistakes
- Saying spontaneous means the decay has no cause at all
- Treating randomness as a constant activity for every sample
- Using λ in hours⁻¹ while labelling A in Bq
What can you explain now?
What does one becquerel represent?
Compare with the explanation
One decay per second
Activity is measured in decays per second.
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Make it stick
Why can a sample have a predictable average decay rate while individual decays remain random?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.