# Radioactive Decay, Half-Life and Safety

> CIE IGCSE Physics · 0625 (2026-2028)
> Source: https://www.owlsprep.com/study/cie-0625-u5-radioactive-decay-half-life-and/

This guide covers all Core and Extended content for radioactive decay, half-life and radiation safety aligned to the CIE IGCSE Physics 0625 2026-2028 syllabus, including worked examples and exam-focused tips.

**Prerequisites:** [Atomic structure and types of ionising radiation](https://www.owlsprep.com/study/cie-0625-u5-atomic-structure-radiation-types/); [Physics graph interpretation skills](https://www.owlsprep.com/study/cie-0625-s1-graph-interpretation-skills/)

## Learning objectives

- Describe the spontaneous, random nature of radioactive decay
- Define half-life and perform Core calculations from decay graphs
- Solve Extended multi-step half-life problems for quantity or time
- Write balanced nuclear decay equations for alpha, beta-minus and gamma emission using nuclide notation (Extended)
- Outline and explain radiation safety procedures for exam questions
- Explain how radiation type and half-life determine the choice of isotope for common uses (smoke alarms, food irradiation, sterilisation, thickness gauges, cancer treatment) (Extended)

## 1. Random Nature of Radioactive Decay (Core)

Radioactive decay is a spontaneous, random process: you cannot predict which individual unstable nucleus in a sample will decay, or exactly when it will happen. The average decay rate for a large enough sample of the same isotope is constant, and is unaffected by external conditions like temperature, pressure, or chemical reactions.

**Radioactive Decay** — The spontaneous breakdown of an unstable atomic nucleus, releasing ionising radiation (alpha, beta, gamma) to form a more stable nucleus.

*Example:* A sample of uranium-238 decays over thousands of years to form lead-206, releasing alpha radiation in the process.

**Worked example:** A student states that we can predict exactly when a single carbon-14 nucleus will decay. Explain why this statement is incorrect, referencing the properties of radioactive decay.

1. 1. State the key property of radioactive decay: it is a random process.
2. 2. Link to individual nuclei: there is no way to predict the decay time of any single unstable nucleus, even if we know the average behaviour of a large sample.
3. 3. Final answer: The statement is incorrect because radioactive decay is random, so we cannot predict the decay time of an individual carbon-14 nucleus.

> **Exam tip:** For 2-mark questions asking for properties of radioactive decay, always list *spontaneous* (happens with no external trigger) and *random* (unpredictable for individual nuclei) to get full marks.

## 2. Half-Life Basics (Core)

**Half-Life** — The average time taken for half the unstable nuclei of that isotope in a sample to decay (equivalently, for the count rate from the sample to halve).

*Notation:* $t_{1/2}$

*Example:* If a sample has a half-life of 2 days, half the original unstable nuclei will remain after 2 days, a quarter after 4 days, an eighth after 6 days, and so on.

For Core level, you calculate half-life from decay graphs or tables, which give count rate (or number of undecayed nuclei) against time. You read the values straight from the graph or table and find the time taken for the count rate to halve. Core half-life calculations will not involve background radiation, so there is no subtraction step (correcting for background is an Extended-only skill, covered later).

**Worked example:** A decay graph shows that the count rate from a radioactive sample is 800 counts per minute (cpm) at the start, 400 cpm after 12 minutes, and 200 cpm after 24 minutes. Calculate the half-life of the sample.

1. 1. Find the time taken for the count rate to fall to half its initial value: $800 \to 400$ cpm, which occurs at 12 minutes.
2. $$t_{1/2} = 12 \text{ minutes}$$
3. 2. Verify: after another 12 minutes (total 24), the count rate halves again from 400 to 200 cpm, confirming the result.

> **Exam tip:** For Core half-life questions, read the values straight from the graph or table and find the time for the count rate (or number of nuclei) to halve. Background correction is an Extended-only skill and will not appear in Core half-life calculations.

## 3. Multi-Step Half-Life Calculations (Extended Only)

Extended learners must solve half-life problems without graphs, using simple step counting to calculate remaining mass, count rate, or time elapsed. No exponential formula is required for the 0625 syllabus: you only need to divide by 2 for each half-life that passes, or multiply by 2 to work backwards from a remaining quantity.

**Worked example:** A radioactive isotope has a half-life of 8 hours. A sample has an initial mass of 96 g of the unstable isotope. Calculate (a) the mass of undecayed isotope remaining after 32 hours, and (b) the total time taken for the undecayed mass to drop to 3 g.

1. Part (a):
2. 1. Calculate number of half-lives in 32 hours: $32 / 8 = 4$ half-lives.
3. 2. Divide initial mass by 2 four times: $96 \to 48 \to 24 \to 12 \to 6$ g.
4. Remaining mass after 32 hours = 6 g.
5. Part (b):
6. 1. Count half-lives to reach 3 g: $6 / 2 = 3$ g, so 1 additional half-life, total 5 half-lives.
7. 2. Total time = $5 \times 8 = 40$ hours.

> **info**
>
> Extended only: Extended half-life questions may give you raw count-rate data from which the background radiation has not been subtracted. In that case you must first subtract the background count rate from every reading, then use the corrected count rates to find the half-life. (Core half-life questions never involve background.)

**Worked example:** A GM tube is used to record the count rate from a radioactive source. The background count rate is measured as 20 cpm. The raw (uncorrected) count rate is 340 cpm at the start and falls to 180 cpm after 6 hours. Calculate the half-life of the source.

1. 1. Subtract the background count rate from each raw reading to get the corrected count rate: start $= 340 - 20 = 320$ cpm; after 6 hours $= 180 - 20 = 160$ cpm.
2. 2. The corrected count rate has halved ($320 \to 160$) in 6 hours, so this is one half-life.
3. $$t_{1/2} = 6 \text{ hours}$$

> **Exam tip:** If you are given a remaining quantity and asked for initial quantity, multiply by 2 once for each half-life that has passed to work backwards. When Extended data is uncorrected, subtract the background count rate from every reading before finding the half-life.

## 4. Radiation Safety Procedures (Core + Extended)

Ionising radiation can damage living cells, causing mutations, cancer, or acute radiation sickness. All safety rules reduce exposure by limiting time near sources, increasing distance from sources, and using shielding to absorb radiation before it reaches people.

- Store sources in lead-lined, clearly labelled containers when not in use
- Handle sources with long tongs or robotic arms to increase distance from the body
- Never point a source at any person, and never eat or drink near radioactive materials
- Wear lead aprons or stand behind lead screens for regular source users
- Limit exposure time to keep total radiation dose as low as possible

**Worked example:** A nuclear power plant worker handles low-level radioactive waste regularly. State three safety precautions they should follow, and explain how each reduces their radiation exposure.

1. 1. Wear a lead apron: lead absorbs gamma and beta radiation, reducing the dose reaching their body cells.
2. 2. Use long handling tongs: increases distance between the worker and the source, reducing exposure significantly (radiation intensity decreases with the square of distance).
3. 3. Wear a dosimeter badge: monitors total cumulative exposure, ensuring they do not exceed legal safe annual dose limits.

> **Exam tip:** When asked to explain safety precautions, always link the precaution to one of the three principles (time, distance, shielding) to get full marks, do not just list the precaution.

## 5. Decay Equations Using Nuclide Notation (Extended Only)

Extended candidates must write balanced nuclear decay equations using nuclide notation $^{A}_{Z}\text{X}$, where $A$ is the nucleon number and $Z$ is the proton number. In every decay equation, the nucleon numbers must balance (the top numbers add up to the same total on both sides) and the proton numbers must balance (the bottom numbers add up to the same total on both sides). This lets you find any unknown daughter nuclide.

Alpha decay: the nucleus emits an alpha particle ${}^{4}_{2}\alpha$ (a helium nucleus), so the nucleon number falls by 4 and the proton number falls by 2.

**Worked example:** Uranium-238, written ${}^{238}_{92}\text{U}$, undergoes alpha decay to form thorium (Th). Write the balanced decay equation.

1. 1. An alpha particle is ${}^{4}_{2}\alpha$, so subtract 4 from the nucleon number and 2 from the proton number: $238 - 4 = 234$ and $92 - 2 = 90$.
2. $${}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\alpha$$
3. 2. Check the balance: nucleon numbers $238 = 234 + 4$; proton numbers $92 = 90 + 2$. The equation balances.

Beta-minus decay ($\beta^-$): inside the nucleus a neutron changes into a proton plus an electron (neutron $\rightarrow$ proton + electron), and the electron is emitted as a beta particle ${}^{\ 0}_{-1}\beta$. The nucleon number is unchanged and the proton number increases by 1.

**Worked example:** Carbon-14, written ${}^{14}_{6}\text{C}$, undergoes beta-minus decay to form nitrogen (N). Write the balanced decay equation.

1. 1. A beta particle is ${}^{\ 0}_{-1}\beta$, so the nucleon number stays the same and the proton number increases by 1: $A$ stays $14$ and $Z = 6 + 1 = 7$.
2. $${}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{\ 0}_{-1}\beta$$
3. 2. Check the balance: nucleon numbers $14 = 14 + 0$; proton numbers $6 = 7 + (-1)$. The equation balances.

Gamma emission ($\gamma$): the nucleus loses surplus energy but emits no particles, so both the nucleon number and the proton number are unchanged. The nuclide is the same element before and after; only its energy decreases (the excited nucleus is marked with an asterisk).

**Worked example:** A nickel-60 nucleus is left in an excited (high-energy) state after a previous decay, written ${}^{60}_{28}\text{Ni}^{*}$. Write the equation for the gamma emission that follows.

1. 1. Gamma radiation ${}^{0}_{0}\gamma$ has no nucleon number and no proton number, so neither number changes.
2. $${}^{60}_{28}\text{Ni}^{*} \rightarrow {}^{60}_{28}\text{Ni} + {}^{0}_{0}\gamma$$
3. 2. Check the balance: nucleon numbers $60 = 60 + 0$; proton numbers $28 = 28 + 0$. The nuclide is unchanged; only energy is released.

> **warning**
>
> For 0625, beta decay always means $\beta^-$ (a neutron becoming a proton). $\beta^+$ decay is not part of this syllabus, and you are not required to mention quarks or neutrinos.

> **Exam tip:** Always check that both the top row (nucleon numbers) and the bottom row (proton numbers) add up to the same total on each side. Use this balance to find any missing nuclide: for alpha subtract 4 and 2; for beta-minus keep $A$ the same and add 1 to $Z$; for gamma both numbers stay the same.

## 6. Choosing Isotopes for Their Uses (Extended Only)

Extended candidates must be able to explain how the type of radiation emitted and the half-life of an isotope decide which isotope is chosen for a job. Two things must be matched to the task: (1) the type of radiation – because alpha, beta and gamma differ in how strongly they ionise and in how far they penetrate or are absorbed by materials; and (2) the half-life – because it sets how long the source stays useful and how quickly its activity falls.

| Application | Radiation used | Why this choice |
| --- | --- | --- |
| Household fire (smoke) alarm | Alpha (α) | α strongly ionises the air so a small current flows between electrodes; smoke absorbs the α particles and the current drops, sounding the alarm. α has a very short range in air, so it is safe outside the alarm. A long half-life means the source lasts for years without replacement. |
| Irradiating food to kill bacteria | Gamma (γ) | γ is very penetrating, so it passes right through the sealed packaging and the food to kill bacteria without making the food radioactive. |
| Sterilising medical equipment | Gamma (γ) | γ penetrates sealed packaging, so equipment can be sterilised after it is packed, killing microbes inside the sealed container. |
| Measuring and controlling material thickness | Beta (β) | β is partly absorbed by thin sheets, so the amount getting through depends on the thickness. α would be fully absorbed (no signal) and γ would pass straight through (insensitive), so only β responds to small thickness changes. A long half-life keeps the reading steady. |
| Diagnosis and treatment of cancer | Gamma (γ) | γ penetrates the body, so it can be aimed at a tumour from outside (treatment) or detected outside the body as a tracer (diagnosis). |

The half-life is chosen for the job as well. A long half-life means the activity stays almost constant, so the source can be used for a long time without replacement (useful for smoke alarms and thickness gauges). A short half-life means the activity falls quickly: this is useful for a medical tracer, so the patient is not exposed for long, but it means the source must be replaced often. So the choice of isotope always balances the radiation type (penetration and absorption) against the half-life (how long the source must stay active).

**Worked example:** Explain why an alpha source with a long half-life is used in a household smoke alarm.

1. 1. Alpha radiation strongly ionises the air between two electrodes, allowing a small current to flow. When smoke enters, it absorbs the alpha particles, the current drops, and the alarm sounds.
2. 2. Alpha has a very short range in air and is stopped by the alarm casing (and by skin), so the source is safe for people in the house.
3. 3. A long half-life means the activity of the source stays almost constant over many years, so the alarm keeps working reliably without the source needing frequent replacement.

**Worked example:** A factory controls the thickness of aluminium foil by passing it between a radioactive source and a detector. Explain why a beta source is used rather than an alpha or a gamma source, and why the source needs a long half-life.

1. 1. Beta radiation is partly absorbed by the thin foil, so the amount reaching the detector depends on the foil thickness. If the foil gets thicker, fewer beta particles get through; if it gets thinner, more get through.
2. 2. Alpha would be completely absorbed by the foil (the detector would read almost nothing), and gamma would pass almost entirely through whatever the thickness (the reading would barely change), so neither could detect small changes in thickness.
3. 3. The detector signal is fed back to the rollers to keep the thickness constant. A long half-life keeps the emitted radiation steady during production, so the reading does not drift as the source decays.

> **Exam tip:** To choose an isotope, match the radiation type to the penetration needed (α stopped very easily, β partly absorbed by thin materials, γ very penetrating) and the half-life to how long the source must stay active. Answers should always give a reason linked to penetration/absorption and to half-life.

## Common pitfalls

- **Wrong:** (Extended) Forgetting that Extended half-life data may be given as raw counts from which background has not yet been subtracted
  - Why it fails: Core half-life calculations never involve background radiation, but Extended questions (5.2.4 Supplement) can give raw uncorrected data, where the background count rate must be subtracted first
  - Correct: For Core, use the values given directly; for Extended raw data, subtract the background count rate from every reading before finding the half-life
- **Wrong:** Using the exponential decay formula $N=N_0e^{-\lambda t}$ for half-life calculations
  - Why it fails: This formula is not part of the CIE IGCSE 0625 syllabus, and you will not get marks for using it even if your answer is correct
  - Correct: Use graph interpretation or simple half-life step counting for all calculations
- **Wrong:** Defining half-life as the time for all nuclei in a sample to decay
  - Why it fails: Half-life describes the time for *half* the unstable nuclei to decay, not all
  - Correct: Define half-life as the average time for the number of unstable nuclei (or count rate) to halve
- **Wrong:** Stating that temperature or pressure affects radioactive decay rate
  - Why it fails: Radioactive decay is a spontaneous nuclear process that is completely unaffected by external conditions
  - Correct: Always note that half-life is constant for a given isotope, independent of external factors
- **Wrong:** Only listing safety precautions without explaining their purpose in exam questions
  - Why it fails: Most 2-3 mark safety questions require both the precaution and a valid explanation for full marks
  - Correct: Link every precaution to how it reduces exposure via limiting time, increasing distance, or adding shielding

## Cheatsheet

| Concept | Core Requirement | Extended Requirement |
| --- | --- | --- |
| Radioactive Decay | Define as spontaneous + random; no external factors affect rate | Same as Core, explain randomness with reference to individual nuclei |
| Half-Life | Calculate from decay graphs or tables using the values given directly (no background correction) | Solve multi-step calculations for remaining quantity, time, or number of half-lives; subtract background first if the data is uncorrected |
| Radiation Safety | List 3+ precautions and explain how they reduce exposure | Same as Core, apply safety rules to specific contexts (medical, industrial, power plants) |
| Uses of Radioisotopes | — | Choose the isotope by radiation type (penetration/absorption) and half-life: smoke alarm α, food irradiation & sterilisation γ, thickness gauge β, cancer diagnosis/treatment γ |

## What's next

This subtopic completes the CIE IGCSE Physics 0625 Nuclear Physics unit: you can now describe the random nature of decay, calculate half-life, write Extended decay equations in nuclide notation, and apply radiation safety. Practice half-life calculations and decay equations using past paper questions to build speed and accuracy, and make sure you clearly distinguish between Core and Extended requirements. Remember that background correction is an Extended-only skill (Core half-life questions never involve background), and always link safety precautions to exposure reduction for full marks.

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