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Physics · Atomic structure
Half-lives and the random nature of radioactive decay
Define half-life, explain how it relates to the random nature of decay, determine half-lives from data, and calculate the net decline after a number of half-lives (Higher tier).
Warm-up
Answer each one, then check.
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1
What does random mean?
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Cannot be predicted
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2
What is half of 800?
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400
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3
What is activity measured in?
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Becquerel (Bq)
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4
What is a count rate?
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Number of counts per second
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5
What does exponential decay look like on a graph?
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A curve that falls quickly then more slowly
Learning Objectives
HALF-LIFE
The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) to fall to half its initial level.
Radioactive decay is random: we cannot say when any one nucleus will decay, but for a large number of nuclei the half-life is predictable.
A Decay Curve
Each half-life the activity halves.
Number of Half-Lives
Higher tier: net decline as a ratio.
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0
Fraction left: 1. Ratio of final to initial: 1 : 1
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1
Fraction left: 1/2. Ratio of final to initial: 1 : 2
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2
Fraction left: 1/4. Ratio of final to initial: 1 : 4
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3
Fraction left: 1/8. Ratio of final to initial: 1 : 8
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4
Fraction left: 1/16. Ratio of final to initial: 1 : 16
Finding a Half-Life from a Graph
The activity of a sample falls from 800 Bq to 400 Bq in 20 minutes and to 200 Bq after 40 minutes. What is the half-life?
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- 1 800 to 400 Halved in 20 minutes
- 2 400 to 200 Halved again in the next 20 minutes
AnswerThe half-life is 20 minutes.
Activity After Several Half-Lives
A source has an activity of 800 Bq and a half-life of 6 hours. Find its activity after 24 hours.
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- 1 Number of half-lives \(24 \div 6 = 4\)
- 2 Halve four times \(800 \rightarrow 400 \rightarrow 200 \rightarrow 100 \rightarrow 50\)
Answer50 Bq
Net Decline as a Ratio (Higher)
Calculate the ratio of the final activity to the initial activity after 3 half-lives.
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- 1 Each half-life Halve the activity
- 2 After 3 \(\left(\tfrac{1}{2}\right)^3 = \tfrac{1}{8}\)
AnswerThe activity falls to 1/8 of its initial value, a ratio of 1 : 8.
Random Decay
How to explain it.
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One nucleus
It is impossible to predict when a particular nucleus will decay.
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Many nuclei
The number decaying in a given time follows a pattern, so half-life is a reliable measure.
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Count rate
Count rate is also random, so it varies slightly between measurements.
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Background
Correct for background radiation to find the true count rate.
Halve It
A sample has a count rate of 640 counts per minute. Its half-life is 3 hours. What is the count rate after 12 hours? What is the ratio of final to initial count rate?
1. Work out the number of half-lives.
2. Halve each time.
A good answer shows: 12 ÷ 3 = 4 half-lives: 640 → 320 → 160 → 80 → 40 counts per minute. The ratio is 1 : 16.
Can I...?
- 1Define half-life.
- 2Explain random decay.
- 3Find half-life from a graph.
- 4Halve repeatedly.
- 5Work out the number of half-lives.
- 6State the ratio after several half-lives.
- 7Explain why decay is random.
- 8Use correct units.
Summary & Exam Focus
- Half-life: time for activity to halve.
- Random decay but a predictable half-life for many nuclei.
- After n half-lives: fraction (1/2)ⁿ.
- Read half-life from a graph.
Exam focus
A radioactive source has a half-life of 20 minutes and an activity of 800 Bq. Find its activity after 60 minutes. (2 marks) (2 marks)
Three half-lives: halve three times.
Key terms
The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.
- Half-life
- The time for the number of nuclei (or the activity) to halve.
- Random
- Cannot be predicted for a single nucleus.
- Count rate
- The number of decays detected each second.
- Activity
- The rate of decay of a source, in becquerel.
- Decay curve
- A graph showing how activity falls with time.
- Background
- The radiation that is always around us.
Practice questions
Have a go at each one before you open its answer.
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Question 1 State 2 marks
What is meant by the half-life of a radioactive isotope?
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Model answer
The time it takes for the number of nuclei in a sample to halve, or the time for the count rate (activity) to fall to half its initial value.
Mark scheme
- Time for the number of nuclei to halve — 1 mark
- or activity or count rate falls to half — 1 mark
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Question 2 Use the graph 4 marks
The graph shows how the activity of a radioactive source changes with time. (a) Determine the half-life of the source. (b) Calculate the activity after 100 minutes.
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Model answer
(a) The activity halves from 800 Bq to 400 Bq in 20 minutes, so the half-life is 20 minutes. (b) 100 minutes is 5 half-lives: 800 → 400 → 200 → 100 → 50 → 25 Bq.
Mark scheme
- Reads 400 Bq at half of 800 — 1 mark
- 20 minutes — 1 mark
- 5 half-lives — 1 mark
- 25 Bq — 1 mark
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Question 3 Calculate 3 marks
A radioactive sample has an activity of 800 Bq. Its half-life is 6 hours. Calculate the activity after 24 hours.
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Model answer
24 ÷ 6 = 4 half-lives; 800 ÷ 16 = 50 Bq
Mark scheme
- 4 half-lives — 1 mark
- Halves four times — 1 mark
- 50 Bq — 1 mark
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Question 4 Calculate 3 marks
The count rate from a radioactive source falls to one eighth of its original value in 15 hours. Calculate the half-life of the source. Also state the net decline as a ratio.
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Model answer
1/8 is 3 half-lives, so 15 ÷ 3 = 5 hours. The ratio of final to initial count rate is 1 : 8.
Mark scheme
- 1/8 means 3 half-lives — 1 mark
- 5 hours — 1 mark
- Ratio 1 : 8 — 1 mark
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Question 5 Explain 2 marks
Radioactive decay is a random process. Explain what this means.
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Model answer
It is not possible to predict when a particular nucleus will decay.
Mark scheme
- Cannot predict which nucleus — 1 mark
- Or when it will decay — 1 mark
Quick check
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After one half-life the activity is...
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C: half
It halves.
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After two half-lives the activity is...
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D: one quarter
(1/2)² = 1/4.
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A source of 400 Bq has a half-life of 2 days. After 6 days it has...
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A: 50 Bq
Three half-lives: 400 → 200 → 100 → 50.
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Radioactive decay is...
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B: random
You cannot predict a single decay.
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After 3 half-lives the ratio of final to initial activity is...
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C: 1 : 8
(1/2)³ = 1/8.
Downloads
Free to keep, print and annotate.
- Half-lives and the random nature of radioactive decay.pptx Built from the lesson script on 30 September 2026. View
- Half-lives and the random nature of radioactive decay - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Half-lives and the random nature of radioactive decay - Exam Questions.docx Built from the lesson script on 30 September 2026. View
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