Radioactivity and half-life: revision notes and practice

What you will learn

• Explain random decay and the statistical meaning of half-life.
• Subtract background and distinguish detector count rate from source activity.
• Predict permitted half-life changes and evaluate supervised measurements.

Key rules

Correct background first

Source-only count rate = detector count rate − mean background count rate, using the same units and measurement conditions.

Use half-life

After one half-life the expected source-only count rate halves. Repeated halvings are used only in General/Higher questions in this app.

Distinguish units

Detector count rate in counts/s or counts/min is not automatically source activity in Bq. One Bq means one nuclear decay per second.

Worked examples

Example 1: A detector measures 90 counts/min; background is 10 counts/min. Find corrected rate.

1. Subtract background from the detector reading.
2. 90 − 10 = 80.

80 counts/min

Example 2: Corrected count rate is 80 counts/min. Predict it after one half-life.

1. One half-life halves the expected corrected rate.
2. 80 ÷ 2 = 40.

40 counts/min

A practice question

A source initially has a background-corrected count rate of 368 counts/min. Its half-life is 6 minutes. Predict its mean background-corrected count rate after 24 minutes.

1. Radioactive decay begins in an unstable nucleus

An unstable atomic nucleus may emit radiation as it changes into a more stable form. Alpha radiation consists of helium nuclei, beta radiation includes fast electrons in the GCSE beta-minus model, and gamma radiation is electromagnetic radiation from the nucleus. These emissions have different ionising and penetrating properties. Radioactive decay changes the nucleus rather than being an ordinary chemical reaction.

A single nucleus decays randomly: its exact decay time cannot be predicted. For a large collection, a statistical pattern emerges because each undecayed nucleus has a characteristic chance of decaying in a given interval. Normal changes of temperature, pressure or chemical state do not provide a way to schedule which nucleus decays next.

2. Activity and detector count rate are distinct

Activity is the number of nuclear decays per second in the source, measured in becquerels. One becquerel means one decay per second. A detector count rate is how many events that particular detector registers per unit time. It can be recorded in counts per second or counts per minute. These quantities are related but are not automatically numerically equal.

Some emitted radiation travels away from the detector, some may be absorbed before reaching it, and detector efficiency is limited. Background radiation can add extra counts. Unless a detection model is supplied, report an answer calculated from detector readings as a count rate, not as a source activity in becquerels. Keep detector position fixed when comparing readings.

3. Measure and subtract the background

Background radiation is present even when the studied source is absent. It comes from several natural sources, including rocks and cosmic radiation, and may also include human-made contributions. Measure a mean background rate under the same counting conditions without the source. Subtract that rate from the detector reading with the source present to estimate the source-only count rate.

For example, a detector reading of 110 counts per minute with a mean background of 14 counts per minute gives a corrected source rate of 96 counts per minute. Subtract rates with the same units. If readings are total counts for an interval, divide by that interval to obtain comparable rates or use equal counting durations. A noisy reading below background does not represent a negative physical source activity.

corrected source count rate = measured detector rate − mean background rate

4. Interpret half-life correctly

Half-life is the time for the expected number of undecayed nuclei in a sample, or its activity, to halve. Under fixed detection conditions, the background-corrected detector count rate follows the same expected halving pattern. A corrected rate of 80 counts per minute becomes an expected 40 counts per minute after one half-life. The measured value may differ because actual decays fluctuate randomly.

Half-life is not the time for every nucleus to decay. Nor does the same fixed number of nuclei disappear during every half-life interval: it is the same fraction of those remaining. Named Foundation courses in this app use one-half-life predictions, background correction and qualitative or practical reasoning. General and Higher practice also uses repeated-halving calculations.

5. Repeated halving uses the remaining amount

For General or Higher questions, first find how many half-life intervals have elapsed by dividing elapsed time by the half-life. If the half-life is six minutes, eighteen minutes is three intervals. Starting from 160 corrected counts per minute, the sequence is 160, 80, 40, 20. After three intervals, the expected corrected rate is 20 counts per minute, not 160 minus three equal reductions.

Perform the calculation on the corrected source rate, then add background back only if asked for the expected raw detector reading. With background 10 counts per minute, a corrected prediction of 20 becomes a detector prediction of 30 counts per minute. The background is not part of the decaying sample and should not be halved alongside it.

General/Higher: corrected rate after n half-lives = initial corrected rate ÷ 2ⁿ

6. Find a half-life from data and handle fluctuations

From corrected data, choose a count-rate value and locate a later time where its expected trend has halved. The difference between the two times estimates the half-life. Do not confuse the later time with the interval. On an experimental plot, a smooth best-fit decay trend can be more informative than forcing the curve through every fluctuating point.

Repeat counts or use suitable longer counting intervals to reduce relative random fluctuations. Longer intervals improve the statistical estimate but must still be appropriate when the source is changing quickly. Keep the geometry, detector settings and timing procedure consistent. Explain how each decision improves comparability or uncertainty rather than merely listing repeat or make accurate as unexplained instructions.

7. Understand protection and supervised measurements

Ionising radiation can damage living tissue. Irradiation means exposure to radiation from a source outside the body; contamination means radioactive material itself is transferred onto or into an object or person. Removing an external source ends that irradiation, whereas contamination may continue irradiating tissue until the material is removed or decays. These terms describe different situations and need different responses.

Practical work with a real source belongs in a properly supervised school procedure with approved equipment. Do not obtain, open or handle radioactive material yourself. Follow the teacher’s controls for handling, distance, shielding and exposure time. This app’s questions are written models and do not require an experiment at home. Use reliable measured or supplied data to practise the reasoning safely.

8. Judge claims from limited measurements

A single count above an earlier reading does not show that the sample has gained undecayed nuclei. Statistical fluctuations can make adjacent short readings increase even while the expected overall rate decreases. Look for a trend across several comparable readings, state the uncertainty and consider whether the background estimate or detector geometry changed. Avoid treating every point as an exact theoretical prediction.

A sample does not become completely inactive after a finite number of half-lives simply because a rounded calculator display shows zero. The expected remaining population becomes small, and actual individual decays still occur randomly. Report an expected rate with appropriate precision and explain any measurement limit. Half-life is a useful statistical model, not a promise that every detector reading equals a precise calculated value.

Check your understanding

How to earn the marks

• Correct background before analysing a source-only decay.
• Keep counts/min, counts/s and Bq distinct.
• Treat predictions as expected means because individual decays are random.
• Use the selected course’s permitted half-life methods and explain practical controls.

A common mistake

Background does not decay with the source. Correct it before analysing a half-life, then add it back only for a predicted detector reading.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.4.2.1–4.4.2.3; 4.4.3.1

  Half-life definitions and finding a half-life from information are available at Foundation. Net-decline ratios after several half-lives are Higher-only; Foundation tasks use single-halving or data interpretation.

• Edexcel GCSE Physics — 6.10–6.16; 6.23–6.27

  Simple half-life calculations and graph interpretations are available at Foundation. The specification marks net-decline ratios over several half-lives as Higher content; those ratio tasks are excluded from Foundation practice.

• OCR Gateway GCSE Physics A — P6.1d–P6.1g; P6.1j–P6.1l

  Half-life concepts and data interpretations are available at Foundation. P6.1k, net decline as a ratio after integral half-lives, is Higher-only.

• OCR Twenty First Century GCSE Physics B — P5.1.7–P5.1.12; P5.2.1

  Half-life concepts and activity–time graph interpretation are available at Foundation. P5.1.11, net-decline ratios after integral half-lives, is Higher-only.

Keep your next step small

Try five questions, read the feedback, and revisit one thing you found difficult. The app tracks a 20-answer practice goal separately from accuracy.

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