Home › Learning Hub › IGCSE Physics › 5b Radioactivity
Topic 5 · 5.2

Radioactivity and half-life

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Know what background radiation is and its main sources; measure count rate; correct for background EXTENDED.
  • Describe emission as spontaneous and random; identify alpha, beta and gamma by nature, ionising effect and penetration; describe their deflection EXTENDED.
  • Describe radioactive decay; use decay equations and explain why some nuclei are unstable EXTENDED.
  • Define half-life and use it in calculations; find half-life from data with background; choose isotopes for uses EXTENDED.
  • State the effects of ionising radiation on living things and describe safe handling; explain precautions EXTENDED.

📚The physics

Detecting radiation

Background radiation is the ionising radiation always present around us. Significant sources are radon gas in the air, rocks and buildings, food and drink, and cosmic rays. Ionising radiation is measured with a detector (such as a Geiger–Müller tube) connected to a counter; the count rate is given in counts/s or counts/minute. EXTENDED Measure the background count with no source present and subtract it from every reading to get the corrected count rate.

Alpha, beta and gamma

Radioactive emission is spontaneous (nothing triggers it) and random in direction and timing.

alpha (α): a helium nucleus (2 protons, 2 neutrons), charge +2; strongly ionising; stopped by paper or a few cm of air
beta (β): a fast electron from the nucleus, charge −1; moderately ionising; stopped by a few mm of aluminium
gamma (γ): electromagnetic radiation, no charge; weakly ionising; only reduced by thick lead or concrete
A source emits alpha, beta and gamma radiation. Alpha is stopped by a sheet of paper, beta by a few millimetres of aluminium, and gamma is only reduced by thick lead.
The more strongly ionising the radiation, the less penetrating it is.

EXTENDED Alpha particles are the most ionising because they are heavily charged (+2) and move relatively slowly with a large kinetic energy, so they interact with many atoms in a short distance. Gamma rays have no charge, so they rarely ionise.

Alpha, beta and gamma radiation pass between two oppositely charged plates in a vacuum. Beta, being negative and light, is strongly deflected towards the positive plate; alpha, positive and heavy, is slightly deflected towards the negative plate; gamma is not deflected.
EXTENDED Alpha and beta bend opposite ways; gamma goes straight on.

Radioactive decay

Radioactive decay is a change in an unstable nucleus that emits alpha or beta particles and/or gamma radiation; it is spontaneous and random. In alpha or beta decay the nucleus becomes a different element. EXTENDED Isotopes may be radioactive because they have too many neutrons or are too heavy; decay makes the nucleus more stable. In beta decay a neutron changes into a proton and an electron: neutron → proton + electron.

\[ {}^{226}_{88}\mathrm{Ra} \rightarrow {}^{222}_{86}\mathrm{Rn} + {}^{4}_{2}\alpha \qquad {}^{14}_{6}\mathrm{C} \rightarrow {}^{14}_{7}\mathrm{N} + {}^{\;0}_{-1}\beta \]

EXTENDED Alpha decay: A falls by 4 and Z by 2. Beta decay: A unchanged, Z rises by 1. Gamma emission: no change in A or Z (the nucleus loses energy).

Half-life

The half-life of an isotope is the time taken for half the nuclei of that isotope in any sample to decay (so the count rate halves).

A decay curve of count rate against time, starting at 800 counts per minute and levelling towards a background of 20 counts per minute. Reading lines show 410 counts per minute at 2.5 minutes and 215 at 5.0 minutes, so the half-life is 2.5 minutes once the background is subtracted.
EXTENDED Always subtract the background before halving.

Uses EXTENDED

  • Smoke alarms: an alpha source with a long half-life (americium-241, 432 years) ionises air between plates; smoke absorbs the alpha particles, the current falls and the alarm sounds.
  • Irradiating food and sterilising equipment: gamma rays kill bacteria, penetrating the packaging.
  • Measuring and controlling thickness: the radiation chosen must be partly absorbed by the material (beta for paper, gamma for steel sheet).
  • Diagnosis and treatment of cancer: gamma emitters; tracers need a short half-life so the patient is not exposed for long.
Paper passes between rollers with a beta source above and a detector below. If the paper becomes thicker it absorbs more beta, the count falls and the rollers are adjusted. Beta is used because alpha would not get through and gamma would pass almost unchanged.
EXTENDED The half-life must be long, so the count does not fall because of decay.

Safety

Ionising radiation can cause cell death, mutations and cancer. Sources are moved and used with tongs, kept pointing away from people, and stored in lead-lined boxes. EXTENDED Precautions work by reducing exposure time, increasing the distance between the source and living tissue, and using shielding to absorb the radiation.

✏️Worked example

Use the decay curve above. The background count is 20 counts/min. (a) EXTENDED Determine the half-life. [2] (b) Predict the corrected count rate after 10 min. [2] (c) Iodine-131 has a half-life of 8 days. What fraction of a sample remains after 24 days? [2]

(a) Corrected initial rate = 800 − 20 = 780; half is 390, so the reading is 390 + 20 = 410, reached at 2.5 min. (Check: 215 − 20 = 195 = 780/4 at 5.0 min.)

(b) 10 min is 4 half-lives: 780 × (½)4 = 49 counts/min (48.75).

(c) 24 / 8 = 3 half-lives: (½)3 = 1/8.

Check it. Two different half-life readings from the same curve should agree: 0 → 2.5 min and 2.5 → 5.0 min both halve the corrected rate.
Halving the raw reading. 800 ÷ 2 = 400 gives about 2.6 min — close, but wrong; with larger backgrounds the error is much bigger.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Theory.) Complete a table for alpha, beta and gamma: the nature of each emission and its charge. [3] (Modelled on 0625/32 June 2026 Q9(a).)
Alpha: helium nucleus, +2. Beta: electron (from the nucleus), −1. Gamma: electromagnetic radiation, 0.
2. (Theory.) EXTENDED A sample contains 24 μg of strontium-90 (half-life 29 years). Sketch the mass–time graph for 90 years, and state the mass after 58 years. [3] (Modelled on 0625/42 June 2026 Q9(a)(ii).)
A smooth curve falling from 24 μg, getting less steep and never reaching zero, through 12 μg at 29 years and 6.0 μg at 58 years (and about 2.8 μg at 90 years). After 58 years: 6.0 μg.
3. (Multiple choice.) EXTENDED A source has a half-life of 6.0 hours. With the source present a detector reads 330 counts/min; the background is 30 counts/min. What is the count rate due to the source after 6.0 hours? A: 135. B: 150. C: 165. D: 180 counts/min.
B. Source alone: 330 − 30 = 300; after one half-life: 150.
4. (Theory.) EXTENDED Polonium-210 (Z = 84) emits an alpha particle. Write the decay equation, the product being lead (Pb). [2]
\( {}^{210}_{84}\mathrm{Po} \rightarrow {}^{206}_{82}\mathrm{Pb} + {}^{4}_{2}\alpha \).
5. (Theory.) State two sources that make a significant contribution to background radiation. [2]
Any two: radon gas in the air; rocks and buildings; food and drink; cosmic rays.
6. (Multiple choice.) A hospital worker wears a lead apron near a radioactive source. How does it protect her? A: it increases her distance from the source. B: it reduces her exposure time. C: it absorbs some of the radiation. D: it reflects the radiation.
C. Shielding.
7. (Theory.) EXTENDED Explain why an alpha source with a long half-life is used in a smoke alarm. [3]
Alpha ionises the air strongly (so there is a measurable current) but is stopped by smoke particles, so the current falls when smoke enters; it is stopped by the casing, so it is safe; a long half-life means the source lasts for many years without being replaced.
8. (Theory.) EXTENDED Describe what happens in a nucleus during beta decay. [2]
A neutron changes into a proton and an electron; the electron is emitted as the beta particle, so the proton number increases by 1 and the nucleon number is unchanged.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Alpha Decay”, “Beta Decay” and “Radioactive Dating Game”
  • UK Health Security Agency — radon and background radiation