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IGCSE Physics notes · Atomic physics

Radioactivity

Radioactive decay changes unstable nuclei randomly. Compare radiation by its nature, ionisation and penetration, and subtract background before interpreting measured half-life data.

By Dr Desouky Physics AcademyUpdated 25 September 202611 min reading + practice

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In this lesson
  1. 01The key idea
  2. 02Distinguish the nucleus from the electron cloud
  3. 03Link penetration and ionisation to particle properties
  4. 04Correct the count rate before looking for halves
  5. 05Conserve nucleon number and charge in decay equations
  6. 06Key definitions
  7. 07Equations & units
  8. 08Worked examples
  9. 09Practice & solutions
  10. 10Common mistakes
  11. 11Quick quiz
  12. 12Questions, explained
  13. 13Learning checklist
  14. 14Sources & citation

The key idea

Compare alpha, beta and gamma radiation, interpret random decay using large samples, and calculate half-life from background-corrected data. Nuclear equations track changes to the nucleus; safety explanations must distinguish irradiation from contamination.

Understand it · 01

Distinguish the nucleus from the electron cloud↗

The proton number identifies the element, while the nucleon number counts protons plus neutrons in its nucleus. Isotopes of the same element have the same proton number but different neutron numbers. Their chemical behaviour can be similar because a neutral atom’s electron arrangement depends mainly on proton number, while their nuclear stability can differ. Nuclear decay changes the nucleus rather than simply moving an outer electron between energy levels.

Radioactive decay is spontaneous: an unstable nucleus does not need to be triggered by heating or a chemical reaction. It is also random: you cannot predict which individual nucleus will decay next. A large collection can nevertheless show a predictable statistical pattern. Activity counts decays per second and is measured in becquerels; a detector count rate is the number of events the apparatus actually records per second or minute.

Pause & explain

Two atoms have the same proton number but different nucleon numbers. What are they, and which particle count must differ?

Check your reasoning

They are isotopes of the same element, and their numbers of neutrons differ.

Understand it · 02

Link penetration and ionisation to particle properties↗

Alpha radiation consists of helium nuclei, containing two protons and two neutrons. It is strongly ionising and has a short range in air. Beta-minus radiation consists of fast electrons produced in nuclear decay; these are not simply electrons knocked out of the atom’s outer shell. Gamma radiation is electromagnetic radiation emitted from the nucleus and has no charge or rest mass.

Alpha is stopped by paper or the outer skin layer, while a suitable thickness of aluminium strongly reduces beta. Gamma is more penetrating and requires substantial shielding, such as thick lead or concrete, to reduce its intensity. Shielding attenuates gamma radiation rather than establishing one universal thickness that stops every photon. All three can be hazardous, with the exposure route affecting which radiation is most significant.

Alpha is stopped at paper, beta passes paper but is stopped by aluminium, and gamma penetrates both and is reduced by thick lead.
Figure 2. These are comparative shielding patterns, not a scale drawing or a guarantee that a particular thickness removes all radiation.Open full-size SVG diagram ↗

Understand it · 03

Correct the count rate before looking for halves↗

Half-life is the time for the number of undecayed nuclei, or the activity of a large sample, to fall to half its current value. Each successive half-life halves what remains: after three half-lives one eighth remains, not one third. A half-life is not a deadline at which every nucleus has decayed. The decay curve falls progressively more slowly because fewer undecayed nuclei remain.

A detector also records background radiation from its surroundings. Subtract the mean background count rate before comparing the source’s values. The measured counts fluctuate randomly, so take readings over adequate time intervals and repeat when practical. Keep the source–detector distance and shielding arrangement constant; changing the geometry can change the count rate even if the source activity follows exactly the same decay pattern.

Pause & explain

A measured count rate is 94 counts/min and background is 14 counts/min. What total reading is expected after one half-life?

Check your reasoning

The source contribution is 80 counts/min, which halves to 40. Add background again: the expected total is 54 counts/min.

Understand it · 04

Conserve nucleon number and charge in decay equations↗

In alpha decay the daughter nucleus has a nucleon number smaller by four and a proton number smaller by two. In beta-minus decay a neutron changes into a proton while an electron is emitted, so the daughter’s nucleon number stays the same and its proton number rises by one. Gamma emission changes the nucleus’s energy without changing either number. Balance the totals on both sides instead of memorising an element change in isolation.

A useful source must match its purpose. A tracer should emit radiation that can be detected outside the monitored region, with a half-life suitable for the measurement rather than unnecessarily long. An absorbed or inhaled alpha emitter can be especially damaging because of strong local ionisation. Distinguish irradiation, exposure to radiation, from contamination, radioactive material being deposited on or inside something. Removing an external source ends that irradiation; contamination may remain.

Key definitions

Isotopes
Atoms of the same element with the same number of protons but different numbers of neutrons.
Half-life
The time taken for half the nuclei in a sample of a radioactive isotope to decay — or for the activity to fall to half its original value.
Radioactive decay
The spontaneous and random emission of radiation from an unstable nucleus. It is unaffected by temperature, pressure or chemical state.
Background radiation
The radiation present everywhere, from rocks, cosmic rays, food and medical sources — subtracted from measurements before analysis.

Equations, units & conditions

Alpha decay

nucleon number −4, proton number −2

Beta decay

nucleon number unchanged, proton number +1

Open the IGCSE Physics formula sheet →

Worked examples, step by step

Example 1

The activity of a sample falls from 1200 Bq to 150 Bq in 12 days. Calculate the half-life.

Follow the method

  1. Count the halvings: 1200 → 600 → 300 → 150. That is 3 half-lives.
  2. 3 half-lives = 12 days.
  3. Half-life = 12 ÷ 3.

Half-life = 4 days

Practice questions with worked solutions

Try each question on paper before opening the solution. These are original academy questions; the suggested marks are a self-checking guide, not an official exam-board mark scheme. Difficulty labels describe this practice set, not predicted grades.

  1. Starter · 4 suggested marks

    1. Subtract background first

    A detector records 172 counts/min initially and 52 counts/min after 12 hours. Background is constant at 12 counts/min. Find the half-life.

    Show solution and self-check: question 1
    1. Subtract background: source rates are 160 and 40 counts/min.
    2. 160 → 80 → 40 is two half-lives.
    3. Each half-life is 12/2 = 6 hours.

    6 hours.

    Self-check · one mark per point

    • Subtract background from the initial reading.
    • Subtract background from the final reading.
    • Identify two halvings.
    • Calculate a 6-hour half-life.
  2. Build · 3 suggested marks

    2. Balance alpha decay

    A nucleus with nucleon number 218 and proton number 84 emits an alpha particle. State the daughter’s nucleon number, proton number and neutron number.

    Show solution and self-check: question 2
    1. Alpha emission removes four nucleons and two protons.
    2. Daughter nucleon number = 218 − 4 = 214; proton number = 84 − 2 = 82.
    3. Neutron number = 214 − 82 = 132.

    Nucleon number 214; proton number 82; neutron number 132.

    Self-check · one mark per point

    • Obtain nucleon number 214.
    • Obtain proton number 82.
    • Calculate neutron number 132.

Common mistakes & how to avoid them

  • Omitting 'random and spontaneous'. Decay cannot be predicted for any individual nucleus and is unaffected by external conditions — a recurring assessment point.
  • Forgetting to subtract background count rate before finding a source's half-life. Corrected readings may still fluctuate because decay and detection are random; they need not halve perfectly in real measurements.
  • Mixing the penetration order: alpha is stopped by paper, beta by a few millimetres of aluminium, gamma reduced by thick lead. Ionising power runs the other way — alpha is by far the most ionising.
  • Choosing the wrong isotope in application questions: medical tracers need gamma emitters with short half-lives (detectable outside the body, quickly gone); paper-thickness gauges need beta (alpha would be stopped, gamma barely affected).

Test yourself

10 questions · instant marking

Question 1 of 10

Which radiation is stopped by a sheet of paper?

Question 2 of 10

A beta particle is:

Question 3 of 10

The most penetrating radiation is:

Question 4 of 10

Radioactive decay is described as:

Question 5 of 10

A sample's activity falls from 800 Bq to 100 Bq in 15 days. Its half-life is:

Question 6 of 10

After alpha decay, the nucleon number of a nucleus:

Question 7 of 10

After beta decay, the proton number of a nucleus:

Question 8 of 10

Isotopes of an element have the same number of:

Question 9 of 10

The best radiation source for a paper-thickness gauge is:

Question 10 of 10

Before analysing radioactivity data, you should subtract:

Understand the why

Questions, explained

Start with the short answer, then follow the reasoning. Each explanation has a permanent link you can share with a classmate or return to when revising.

  1. What are the properties of alpha, beta and gamma radiation?
  2. How do you calculate half-life from a graph?
  3. Why is gamma used for medical tracers?
  4. Does all radioactive material disappear after two half-lives?
  5. What is the difference between irradiation and radioactive contamination?
  6. How can beta-minus radiation be an electron if it comes from the nucleus?
Browse all physics questions →

What are the properties of alpha, beta and gamma radiation?

Alpha is a helium nucleus, beta-minus is a fast electron emitted in nuclear decay, and gamma is electromagnetic radiation. Alpha is strongly ionising with low penetration; gamma is more penetrating and less densely ionising. Their charge and mass differences also affect deflection in fields.

Compare the same property across the three types rather than mixing unrelated facts. Alpha carries charge +2e, beta-minus carries −e, and gamma is uncharged. This explains why gamma is not deflected by electric or magnetic fields in the standard treatment. Paper stops alpha, suitable aluminium shielding strongly reduces beta, and thick lead or concrete reduces gamma intensity. The shielding comparison depends on radiation energy and material thickness, so gamma should not be described as absolutely unstoppable or completely removed by one universal sheet thickness.

  • Read the supporting explanation ↑

How do you calculate half-life from a graph?

For a source-activity graph, find the time taken to fall from any chosen activity to half that value. For measured detector count rate, subtract background first. Check several intervals where possible, allowing for random fluctuations and reading uncertainty rather than requiring exact halves.

A graph starting above zero does not automatically represent source activity alone. If background is present, half of the total initial reading is not the correct target. Subtract background to isolate the source contribution, halve that contribution, then add background back when locating the target on the original total-count graph. Draw clear horizontal and vertical guides to read times. A long straight segment drawn between noisy points is less informative than a sensible decay trend, and an apparent small variation between half-life estimates may reflect measurement uncertainty.

A decay curve tends towards a constant background level; guides show the source component halving after equal time intervals.
Subtract background count rate before finding how long the source count rate takes to halve.Open full-size SVG diagram ↗

Read a total-count graph

Initial total count rate is 110 counts/min, including 10 counts/min background. What total count rate corresponds to one half-life?

  1. Initial source rate = 110 − 10 = 100 counts/min.
  2. After one half-life the source gives 50 counts/min.
  3. Add the unchanged background: 50 + 10 = 60 counts/min.

Look for 60 counts/min on the total-count graph.

  • Read the supporting explanation ↑

Why is gamma used for medical tracers?

Gamma radiation can escape the monitored region and be detected outside the body, making suitable gamma-emitting isotopes useful tracers. The isotope’s half-life must be long enough for the investigation but short enough to avoid unnecessarily persistent activity. Biological behaviour also matters in selecting an actual tracer.

The exam explanation links penetration to detection: radiation stopped entirely inside the body would not reach an external detector effectively. A useful tracer must also travel to the region being investigated, so its chemistry and biological handling cannot be ignored in real applications. “Short half-life” is relative to the measurement time; an isotope that decays almost completely before it arrives would not be useful. Gamma exposure still requires controlled use. An external detector records only some emitted photons, so the measured count rate also depends on detector efficiency and geometry.

  • Read the supporting explanation ↑

Does all radioactive material disappear after two half-lives?

After each half-life, half of the undecayed nuclei present at its start remain on average in a large sample. It does not mark a time when every nucleus has decayed. Successive remaining fractions are one half, one quarter, one eighth and so on.

The number that decays during successive equal half-life intervals becomes smaller because there are fewer undecayed nuclei available. This is why a decay curve gradually becomes less steep rather than forming a straight line to zero. Individual nuclei remain unpredictable: a particular nucleus might decay early or persist through many half-lives. In a finite sample, the very last event is a random question, whereas the smooth curve describes statistical behaviour of a large population. Match the remaining fraction to the number of halving steps before calculating the elapsed time.

Find a remaining fraction

What fraction of the initial undecayed nuclei remains after four half-lives?

  1. After successive half-lives: 1/2, 1/4, 1/8, 1/16.
  2. Convert 1/16 to a percentage: 6.25%.

One sixteenth remains, equivalent to 6.25%.

  • Read the supporting explanation ↑

What is the difference between irradiation and radioactive contamination?

Irradiation means exposure to radiation from a source; contamination means radioactive material is deposited on or inside an object. Removing an external source ends that irradiation, while contamination may continue producing exposure until the material is removed or decays.

An object can be irradiated without acquiring any radioactive material. For example, an external source can send radiation towards a sample and then be moved away. By contrast, radioactive dust on a surface remains a source wherever the dust is carried, so it can spread the problem. The distinction matters when explaining protective measures: shielding and distance reduce exposure, while preventing ingestion, inhalation or transfer of material addresses contamination. Do not automatically conclude that every object exposed to radiation becomes radioactive; that is not what ordinary irradiation means.

  • Read the supporting explanation ↑

How can beta-minus radiation be an electron if it comes from the nucleus?

In beta-minus decay, an electron is produced when a neutron in the nucleus changes into a proton. It is not an ordinary shell electron escaping the atom. The daughter nucleus keeps the same nucleon number but its proton number increases by one.

The total count of nucleons stays fixed because one neutron becomes one proton; a nucleon has changed type rather than being removed. The emitted electron carries negative charge, balancing the increase in the daughter nucleus’s positive charge. At IGCSE level, decay equations track nucleon and proton numbers using this relationship. Full nuclear descriptions include an antineutrino, beyond some syllabus treatments. A separate process removing an outer electron would produce an ion of the same element, whereas beta-minus decay changes the proton number and therefore the element.

  • Read the supporting explanation ↑
  • Continue with static electricity →

Your learning checklist

Use these goals to check your understanding. Requirements vary by specification, tier and exam year; the official references below define your full course.

  • Describe the nuclear atom: protons, neutrons, electrons; proton number and nucleon number; isotopes
  • Describe the nature, charge, penetration and ionising power of alpha, beta and gamma radiation
  • Know that radioactive decay is spontaneous and random
  • Define half-life and perform half-life calculations from data or graphs
  • Describe uses (medical tracers, thickness control, dating) and safety precautions
  • Write nuclide equations for alpha and beta decay (Extended)

Course & model notes

In Cambridge 0625, beta radiation refers to beta-minus; beta-plus is not included. Radioactivity calculations and explanation depth should be checked against your Core or Extended route.

Check which exam board you study

Sources & how to cite these notes

Original explanations, illustrations and practice by Dr Desouky Physics Academy. Official specifications guide the course scope; questions and suggested marks on this page are our own revision material.

  • Cambridge IGCSE Physics 0625 — 2026–2028 syllabus
  • Pearson Edexcel International GCSE Physics 4PH1 — specification

Reference this page

Dr Desouky Physics Academy. IGCSE Physics: Radioactivity. Updated 2026-09-25. https://www.drdesouky.com/revision/igcse-physics/radioactivity

Use the arrow beside an explanation heading to link straight to that section. Spotted a problem? Contact the academy with the topic and the step you want us to check.

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