Radioactivity: Complete O Level Physics Cheatsheet
O Level Physics, Chapter 22 · Read time: ~9 minutes
These notes come from TGC Academy's O Level Physics tuition in Singapore.
Key Formulas
The nucleus and isotopes
The nucleus contains protons (positive) and neutrons (no charge), together called nucleons. The proton number Z identifies the element, and the nucleon number A is the total number of protons and neutrons.
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). Some isotopes have unstable nuclei that decay randomly and spontaneously, emitting radiation. You can't predict when a particular nucleus will decay, and decay isn't affected by temperature or pressure.
Background radiation is always present, from rocks and soil, cosmic rays, food and medical sources. Subtract it from detector readings before calculating anything.
Trap: Forgetting background radiation is a classic half-life trap. If a question gives a background count, subtract it from every reading first, then halve. Halving the raw counts gives the wrong half-life.
Alpha, beta and gamma
Alpha (α): a helium nucleus, charge +2. Most strongly ionising, least penetrating: stopped by a sheet of paper or a few cm of air.
Beta (β): a fast-moving electron, charge −1. Moderately ionising and penetrating: stopped by a few mm of aluminium.
Gamma (γ): an electromagnetic wave, no charge. Weakly ionising, most penetrating: only reduced by thick lead or concrete. In electric or magnetic fields, alpha and beta are deflected in opposite directions (beta more strongly, being much lighter), while gamma is not deflected.
Trick: Ionising power and penetrating power always go in opposite order. Alpha is the most ionising and least penetrating, gamma is the least ionising and most penetrating. Learn one ranking and flip it for the other.
Half-life, uses and safety
Half-life is the time taken for half the undecayed nuclei in a sample to decay, which is also the time for the activity (count rate) to halve. After n half-lives, the fraction left is (½)ⁿ.
Uses: alpha in smoke detectors, beta for controlling the thickness of paper or metal sheets, gamma for radiotherapy, sterilising medical equipment and as tracers, and carbon-14 for dating once-living material.
Safety: handle sources with long tongs, never point them at anyone, store them in lead-lined containers, keep exposure time short and distance large. Ionising radiation can damage cells and DNA, leading to cancer.
Trap: After two half-lives, a quarter of the sample remains, not zero. Many students assume 'two halves make a whole'. Always count half-lives one step at a time.
Worked Example
A radioactive source has a half-life of 6 hours. Its count rate, corrected for background radiation, is 800 counts per minute at 9am.
(a) Calculate the corrected count rate at 3am the next day (18 hours later). [2]
18 h ÷ 6 h = 3 half-lives
800 → 400 → 200 → 100
= 100 counts per minute
(b) How long after 9am does the corrected count rate fall to 50 counts per minute? [2]
800 → 400 → 200 → 100 → 50 is 4 half-lives
4 × 6 h = 24 hours
(c) Radium-226 (proton number 88) decays by emitting an alpha particle. State the nucleon number and proton number of the nucleus formed. [2]
Nucleon number: 226 − 4 = 222
Proton number: 88 − 2 = 86
Why this question is a good test of the topic: listing each halving step, rather than jumping straight to an answer, is what earns the method mark. Part (c) checks that you know alpha removes 4 from A and 2 from Z, not the other way round.
Frequently Asked Questions
What is half-life in O Level Physics?
The time taken for half the undecayed nuclei in a sample to decay, or for the count rate to fall to half its value.
Which radiation is the most penetrating?
Gamma radiation. It's only reduced by thick lead or concrete, while alpha is stopped by paper and beta by a few mm of aluminium.
What happens to the nucleus in beta decay?
A neutron changes into a proton and emits a fast electron. The nucleon number stays the same and the proton number increases by 1.
What are isotopes?
Atoms of the same element with the same number of protons but different numbers of neutrons.
Why must background radiation be subtracted?
A detector picks up background radiation as well as the source. Subtracting it gives the source's true count rate, which is the value that halves every half-life.
Need help with half-life and decay equations?
Small group O Level Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.