GCSE Physics revision

Half-lives and the random nature of radioactive decay

Atoms and nuclear radiation

AQA 4.4.2.3

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AQA student objectives

Learning pathway

All · Most · Some

ALL 🎯

Explain the concept of half-life and how it is related to the random nature of radioactive decay.

MOST 🎯🎯

Apply the scientific explanation of half-lives and the random nature of radioactive decay to a relevant example.

SOME 🎯🎯🎯

Analyse a new situation involving half-lives and the random nature of radioactive decay and explain the scientific reasoning.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

What is Radioactivity?

Some materials contain unstable isotopes that emit radiation (alpha particles, beta particles, or gamma rays) in order to become more stable — these materials are called radioactive.
The decay of any individual radioactive nucleus is completely random, so it is impossible to predict exactly when a single nucleus will decay.
When a large enough sample of radioactive isotopes is studied, useful patterns in the overall decay behaviour can be identified.

1. What is Radioactivity?AQA

Notes

Some materials contain unstable isotopes that emit radiation (alpha particles, beta particles, or gamma rays) in order to become more stable — these materials are called radioactive.
The decay of any individual radioactive nucleus is completely random, so it is impossible to predict exactly when a single nucleus will decay.
When a large enough sample of radioactive isotopes is studied, useful patterns in the overall decay behaviour can be identified.

Activity and the Becquerel

Activity is the overall rate of radioactive decay of all the unstable nuclei in a sample.
Activity is measured in becquerels (Bq), where 1 Bq equals 1 radioactive decay per second.
For example, a sample with an activity of 600 Bq has 600 nuclei decaying every second.

Defining Half-Life

Half-life is defined as the time taken for the number of radioactive nuclei in a sample to halve — for example, from 1,000,000 unstable nuclei down to 500,000.
Half-life can also be defined as the time taken for the activity of a sample to halve — for example, from 600 Bq down to 300 Bq.
Both definitions are equivalent because fewer remaining radioactive nuclei directly leads to a lower activity.

3. Defining Half-LifeAQA

Notes

Half-life is defined as the time taken for the number of radioactive nuclei in a sample to halve — for example, from 1,000,000 unstable nuclei down to 500,000.
Half-life can also be defined as the time taken for the activity of a sample to halve — for example, from 600 Bq down to 300 Bq.
Both definitions are equivalent because fewer remaining radioactive nuclei directly leads to a lower activity.

How Activity Changes Over Time

As radioactive nuclei decay, the number of unstable nuclei remaining decreases, so the activity of the sample also decreases over time.
The rate of decline in activity also slows down over time, which is why a graph of activity against time produces a curved (exponential decay) shape rather than a straight line.
Different radioactive materials have different half-lives — a sample that decays more rapidly will have a shorter half-life and a higher initial activity.

4. How Activity Changes Over TimeAQA

Notes

As radioactive nuclei decay, the number of unstable nuclei remaining decreases, so the activity of the sample also decreases over time.
The rate of decline in activity also slows down over time, which is why a graph of activity against time produces a curved (exponential decay) shape rather than a straight line.
Different radioactive materials have different half-lives — a sample that decays more rapidly will have a shorter half-life and a higher initial activity.

Reading a Decay Graph

To calculate the half-life from an activity–time graph, identify the time it takes for the activity to drop to exactly half its original value.
The result can be verified by checking that the activity halves again over the same time interval — for example, dropping from 300 Bq to 150 Bq in the same time as it dropped from 600 Bq to 300 Bq.
For example, if a sample's activity drops from 600 Bq to 300 Bq in 2 hours, the half-life is 2 hours.

5. Reading a Decay GraphAQA

Notes

To calculate the half-life from an activity–time graph, identify the time it takes for the activity to drop to exactly half its original value.
The result can be verified by checking that the activity halves again over the same time interval — for example, dropping from 300 Bq to 150 Bq in the same time as it dropped from 600 Bq to 300 Bq.
For example, if a sample's activity drops from 600 Bq to 300 Bq in 2 hours, the half-life is 2 hours.

Measuring Activity with a Geiger–Müller Tube

In practice, activity is measured using a Geiger–Müller (GM) tube and counter, which detects incoming alpha particles, beta particles, and gamma rays.
The GM tube records the number of detected decays per second as the count rate, which is used to estimate the activity of the radioactive source.

6. Measuring Activity with a Geiger–Müller TubeAQA

Notes

In practice, activity is measured using a Geiger–Müller (GM) tube and counter, which detects incoming alpha particles, beta particles, and gamma rays.
The GM tube records the number of detected decays per second as the count rate, which is used to estimate the activity of the radioactive source.

Calculating Remaining Nuclei After Multiple Half-Lives

To find the number of radioactive nuclei remaining after a given time, first calculate how many half-lives have passed by dividing the total time by the half-life.
Then halve the initial number of nuclei once for each half-life that has elapsed.
For example, if the half-life is 40 hours and the time elapsed is 5 days (120 hours), then
120
40
= 3 half-lives have passed.
Starting from 3,000,000 nuclei and halving three times:
3,000,000 → 1,500,000 → 750,000 → 375,000 nuclei remaining.

7. Calculating Remaining Nuclei After Multiple Half-LivesAQA

Notes

To find the number of radioactive nuclei remaining after a given time, first calculate how many half-lives have passed by dividing the total time by the half-life.
Then halve the initial number of nuclei once for each half-life that has elapsed.
For example, if the half-life is 40 hours and the time elapsed is 5 days (120 hours), then
120
40
= 3 half-lives have passed.
Starting from 3,000,000 nuclei and halving three times:
3,000,000 → 1,500,000 → 750,000 → 375,000 nuclei remaining.

Key Equations and Units to Remember

Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second.
The number of half-lives elapsed is calculated as: Number of half-lives = Total time
Half-life
, ensuring both times are in the same unit.
n
The number of remaining nuclei after n half-lives is: N = N0 × ( 12 ) , where N0 is the initial number of nuclei.

8. Key Equations and Units to RememberAQA

Notes

Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second.
The number of half-lives elapsed is calculated as: Number of half-lives = Total time
Half-life
, ensuring both times are in the same unit.
n
The number of remaining nuclei after n half-lives is: N = N0 × ( 12 ) , where N0 is the initial number of nuclei.