IGCSE Physics: radioactivity, half-life and nuclear equations

Alpha, beta and gamma compared

A is the nucleon (mass) number and Z the proton (atomic) number. Edexcel also asks about neutron emission: A falls by 1, Z unchanged.

Key ideas, board by board

The atom has a small, positive nucleus of protons and neutrons with electrons around it. Isotopes are atoms of the same element (same proton number) with different numbers of neutrons. Both boards use nuclide notation, with the nucleon number written above the proton number before the symbol; in plain text, carbon-14 has A = 14 and Z = 6, so it has 8 neutrons. Cambridge Supplement adds the alpha-scattering evidence for the nuclear model: most alpha particles pass straight through thin gold foil (the atom is mostly empty space), a few are deflected through large angles (a small, dense, positive nucleus).

Cambridge Core covers background radiation and its sources (radon gas, rocks and buildings, food and drink, cosmic rays), detecting radiation with a detector and counter, the nature, ionising effect and penetration of alpha, beta and gamma, decay as spontaneous and random, half-life in simple calculations without background, the effects of radiation on living things, and safe handling and storage. Supplement adds corrected count rate (subtracting background), deflection in electric and magnetic fields, explaining ionising ability by kinetic energy and charge, why some isotopes are unstable, decay equations in nuclide notation, half-life from data that includes background, choosing isotopes for uses such as smoke alarms and thickness gauges, safety in terms of time, distance and shielding, and fission and fusion.

Edexcel 4PH1 section 7 has no P statements, so all of it can appear on either paper. It includes the four main types of radiation (alpha, beta, gamma and neutron), balancing nuclear equations, detection with photographic film or a Geiger-Muller detector, activity in becquerels, half-life calculations including graphical methods, uses in industry and medicine, contamination versus irradiation, dangers and waste disposal, and fission and fusion: U-235 splitting after absorbing a neutron, chain reactions, control rods, moderator and shielding, and why fusion needs very high temperatures and pressures.

Worked example 1: half-life

Question: a sample has an activity of 800 Bq. Its half-life is 6 hours. What is its activity after 24 hours?

Number of half-lives = 24 ÷ 6 = 4. Halve four times: 800 -> 400 -> 200 -> 100 -> 50 Bq. As a fraction, 800 x (1/2)^4 = 800 x 1/16 = 50 Bq.

Reverse version: a count rate falls from 640 to 40 counts per minute in 20 minutes. 640 -> 320 -> 160 -> 80 -> 40 is 4 halvings, so the half-life is 20 ÷ 4 = 5 minutes. From a graph, read the time for the count to fall from any value to half of it, and check with a second pair of points.

Worked example 2: background correction and decay equations

Corrected count rate (Cambridge Supplement): a detector reads 75 counts per minute near a source and 25 counts per minute with the source removed. Corrected count rate = 75 - 25 = 50 counts per minute. Always subtract background before working out a half-life from data that includes it.

Alpha decay: radium-226 (A = 226, Z = 88) emits an alpha particle (A = 4, Z = 2). The new nucleus has A = 226 - 4 = 222 and Z = 88 - 2 = 86, which is radon-222. Check: nucleon numbers 226 = 222 + 4, proton numbers 88 = 86 + 2.

Beta decay: carbon-14 (A = 14, Z = 6) emits a beta particle (A = 0, Z = -1). The new nucleus has A = 14 and Z = 7, which is nitrogen-14. Inside the nucleus, a neutron has changed into a proton and an electron, and the electron is emitted.

Common mistakes

• Saying gamma rays are particles or that they change the nucleus into another element.
• Writing that alpha is the most penetrating because it is the biggest. It is the least penetrating because it is the most strongly ionising and loses its energy quickly.
• Saying the beta particle is an electron from the electron shells. It comes from the nucleus.
• Thinking a sample is safe after two half-lives. A quarter of the original nuclei are still undecayed.
• Forgetting to subtract background count before calculating half-life (Cambridge Supplement).
• Confusing contamination (radioactive material gets onto or into something) with irradiation (exposure to radiation from outside). Irradiated food does not become radioactive.
• Mixing up fission (splitting a large nucleus) and fusion (joining small nuclei).

Exam technique and mark-scheme language

Use the word random correctly: you cannot predict which nucleus will decay next or when. Use spontaneous for decay not affected by temperature or chemical state. When choosing an isotope for a use, link the type of radiation and the half-life to the job: a smoke alarm uses an alpha source because alpha is stopped by smoke particles and has a long half-life so the alarm lasts for years; a medical tracer uses a gamma source with a short half-life so it can be detected outside the body and does not stay active for long.

For safety, Cambridge Supplement expects three ideas: reduce exposure time, increase distance from the source, and use shielding to absorb the radiation. For fission, Edexcel's expected chain is: a U-235 nucleus absorbs a neutron, becomes unstable and splits into two daughter nuclei, releasing two or three neutrons and energy as kinetic energy of the products; the neutrons can cause further fissions, a chain reaction, controlled by control rods absorbing neutrons, while the moderator slows neutrons so they are more likely to be absorbed.

How one-to-one lessons help with this topic

Radioactivity is short but dense with precise vocabulary, and small slips (ionising versus penetrating, contamination versus irradiation) cost marks. A tutor uses quick recall rounds and then exam-style explanation questions, checking each term. Half-life graphs and nuclear equations are practised on the shared whiteboard until the student balances A and Z without hesitating. Lessons follow the student's board, since Cambridge Core students do not need decay equations while every Edexcel student does.

Self-check

1. Describe the structure of an atom and define isotope, proton number and nucleon number.
2. Compare alpha, beta and gamma for nature, charge, ionising effect and penetration.
3. List four sources of background radiation.
4. Write alpha and beta decay equations and check that A and Z balance.
5. Calculate the activity remaining after a whole number of half-lives.
6. Find a half-life from a decay graph.
7. Explain the difference between contamination and irradiation.
8. Describe fission, a chain reaction and the role of control rods and the moderator.