Radioactive decay, half-life, uses and hazards

Key idea: A single nuclear decay is random and spontaneous, but a large population produces predictable statistics. Radiation properties determine both useful applications and hazards.

GCE A-Level H1 Physics 2027

H1 Physics 8867 · Lesson 2 of 3

Check your understanding

By the end of this lesson, you should be able to

Explain randomness from count-rate fluctuations and use activity.
Account for background radiation and compare alpha, beta and gamma radiation.
Use half-life and evaluate applications and hazards through ionisation, penetration and lifetime.

Learn the idea

Big question: How can individual decays be unpredictable while a large sample follows a reliable half-life pattern?

Separate random events from predictable averages

Spontaneous decay needs no external trigger. Random decay means the time at which one nucleus decays cannot be predicted. Repeated counts fluctuate even when source and detector stay fixed; this scatter is evidence of randomness, not necessarily faulty equipment.

For many nuclei, the average activity follows a predictable pattern. Activity is decays per second, measured in becquerels. Half-life is the time for activity or undecayed nuclei to halve, not a promised lifetime for one nucleus.

Check your understanding: A steady source gives counts 101, 94, 108 and 97 in equal intervals. Must its activity be changing?

No. Random fluctuations are expected; look for a sustained trend beyond the scatter.

Choose radiation by property and manage risk

Alpha radiation is a helium nucleus with charge +2e. Beta-minus radiation is a fast electron with charge −e. Gamma radiation is an uncharged electromagnetic photon. Alpha is strongly ionising and weakly penetrating; beta has intermediate properties; gamma is weakly ionising but highly penetrating.

Background radiation comes from cosmic rays, rocks, building materials and naturally occurring isotopes. It must be measured separately and subtracted because it contributes counts even when the source is absent.

A good application argument links property to purpose and then to a safety control. Risk depends on ionisation, penetration, activity, exposure time, distance, shielding and whether material can enter the body.

Check your understanding: Why can an alpha source be especially hazardous if inhaled?

Its short range then lies inside tissue, where its strong ionisation deposits energy densely.

Scroll diagram horizontally to read all labels.

Individual decay times are random, but a large population follows a predictable exponential law: the expected number remaining halves after each half-life.

Key ideas

Activity is decays per second, measured in Bq.
Half-life applies to activity or number of undecayed nuclei, not a guaranteed lifetime for one nucleus.
A source dangerous outside the body may present a different risk if inhaled or swallowed.

Relationships to know

corrected count rate = measured rate − background rate
after n half-lives: x = x₀(1/2)ⁿ

Follow the reasoning

Worked example

Remove background before finding half-life

Question: A detector records 860 counts min⁻¹ initially and 125 counts min⁻¹ after 15 h. Background is 25 counts min⁻¹. Find the half-life.

Step 1: Correct both readings
Why: Background does not decay with the source and distorts ratios.
Working: Initial source rate = 860 − 25 = 835; later source rate = 125 − 25 = 100 counts min⁻¹.
Step 2: Identify the number of halvings
Why: 835 to 100 is close to a factor of 8.35; data fluctuations make exact powers of two unlikely.
Working: After three half-lives, predicted rate is 835/8 = 104 counts min⁻¹, consistent with 100.
Step 3: Find one half-life
Why: Three equal half-life intervals occupy the 15 h.
Working: T½ ≈ 15/3 = 5.0 h.

Answer: The half-life is approximately 5.0 h.

Check: Using raw readings would give a misleading ratio because the 25 counts min⁻¹ background becomes a large fraction of the late reading.

Now try it with support

Practise with support

Choose between alpha and gamma for an external thickness gauge and justify the choice using penetration and ionisation.

Hints

The radiation must pass through the material but change detectably with thickness.
Do not choose only by saying one is ‘stronger’.

View the guided answer

Alpha is usually too weakly penetrating. Gamma can pass through substantial material but may change too little for thin sheets; beta is often appropriate for paper or foil. The best answer depends on thickness and required sensitivity, justified by penetration and detector response.

Your turn

Practise independently

A detector reads 820 counts min⁻¹ initially and 120 counts min⁻¹ after 12 h. Background is 20 counts min⁻¹. Determine the half-life.

Check your answer

Corrected rates are 800 and 100 counts min⁻¹. The activity falls by a factor of 8 = 2³, so three half-lives take 12 h. The half-life is 4.0 h.

Common mistakes and exam guidance

Watch out for

Using raw count rate without subtracting background.
Saying every nucleus decays after exactly one half-life.

In an exam

For an application, link radiation property → useful effect → safety control.
Read a decay curve using repeated halving and keep the same background correction throughout.

Put the ideas together

Exam-style practice [8 marks]

Choose and justify radiation for (a) monitoring aluminium-sheet thickness and (b) sterilising sealed medical equipment. For each, link penetration and ionisation to function and give one safety control. Explain why half-life matters when choosing each source.

Plan before you answer

Reject unsuitable options as well as selecting one.
Use property → effect → control.
Balance usable lifetime against long-lived waste.

View the marking points and model answer

Marking points

Chooses beta for thin aluminium/appropriate intermediate penetration.
Explains count changes measurably with thickness; alpha would be stopped too easily and gamma may be too penetrating.
Gives shielding/distance/controlled enclosure for gauge.
Chooses gamma for sealed-equipment sterilisation/high penetration.
Links ionisation dose to killing microorganisms.
Gives thick shielding/remote handling/time control.
Explains half-life must be long enough for practical stable use.
Explains unnecessarily long half-life creates prolonged disposal/storage hazard or short half-life needs frequent replacement.

Model answer

Beta is suitable for thin aluminium because it partly penetrates the sheet, so detector count falls measurably as thickness increases; alpha would be absorbed too readily and gamma may change too little. Enclose and shield the gauge and limit access. Gamma suits sealed medical equipment because it penetrates packaging and its ionising dose kills microorganisms; use thick shielding and remote handling. In both cases the half-life should be long enough for a steady useful source, but not needlessly long because storage and disposal hazards then persist; a very short half-life would require frequent replacement.

Finish from memory

Three-question recap

What is one becquerel?
Check
One nuclear decay per second.
Why subtract background count rate?
Check
It is not due to the source and would distort its activity and half-life.
What happens after three half-lives?
Check
The activity or undecayed number falls to one eighth of its initial value.

Try this next

Use conservation of nucleon number, charge and mass–energy to write and interpret nuclear reactions.

Continue to Nuclear reactions, mass defect and binding energy Return to Nuclear Physics Review Nuclear atom, nuclides and amount

Continue with the next resource in this course.

Course and syllabus information

Course: GCE A-Level H1 Physics
Edition: GCE A-Level H1 Physics 2027