Radioactivity is one of the last topics in the Pure Physics (5054) syllabus, which means many students meet it only weeks before Prelims. The good news: it is one of the most predictable topics in the whole paper. Decay equations follow two rules. Half-life questions follow one pattern. Once you drill both, these are close to free marks.
Here is exactly how we teach it at Dojo.
Part 1: Decay Equations Are Just Two Conservation Rules
Every nuclear equation in the O-Level syllabus is written in the form:
A/Z X where A = nucleon number (top) and Z = proton number (bottom).
To balance any decay equation, only two things must match on both sides:
- Total nucleon number (top numbers)
- Total proton number (bottom numbers)
That is it. You do not need to memorise long decay chains.
The three emissions you must know cold
| Emission | Symbol | Nucleon number change | Proton number change |
|---|---|---|---|
| Alpha | 4/2 He | decreases by 4 | decreases by 2 |
| Beta-minus | 0/-1 e | no change | increases by 1 |
| Gamma | 0/0 γ | no change | no change |
Worked example: alpha decay
Bismuth-212 (212/83 Bi) emits an alpha particle. Write the equation.
- Nucleon number: 212 − 4 = 208
- Proton number: 83 − 2 = 81
212/83 Bi → 208/81 Tl + 4/2 He
You are given a Periodic Table in the exam, so use it to find the element with proton number 81 (thallium). Marks are usually awarded for the correct numbers, so even if you name the element wrongly, get 208 and 81 right.
Worked example: beta decay
Carbon-14 emits a beta particle.
14/6 C → 14/7 N + 0/−1 e
A very common exam follow-up: "Explain how a nucleus can emit an electron when the nucleus contains only protons and neutrons."
Mark-scheme answer: a neutron in the nucleus changes into a proton and an electron, and the electron is emitted.
Part 2: Half-Life, Say It the Way the Mark Scheme Says It
Definition marks are lost every year because students are vague. Learn one of these two phrasings word for word:
- The half-life is the time taken for half the unstable nuclei in a sample to decay.
- The half-life is the time taken for the activity (or count rate) of a sample to fall to half its original value.
Avoid writing "time for half the sample to disappear" or "half the atoms to die". Those get zero.
The standard calculation pattern
Almost every numerical half-life question is: count the number of halvings.
Example: A source has an activity of 800 Bq. Its half-life is 6 hours. How long until the activity falls to 50 Bq?
800 → 400 → 200 → 100 → 50 is 4 halvings.
Time = 4 × 6 = 24 hours.
Working backwards is just as common: if a sample now has 25 g of an isotope and 3 half-lives have passed, the original mass was 25 × 2³ = 200 g.
When the numbers are not neat
Use the relationship:
A = A₀ × (1/2)^(t / T)
where T is the half-life. For example, if A₀ = 640 Bq, T = 10 min and t = 25 min, then A = 640 × (1/2)^2.5 = 113 Bq (3 s.f.). If the question gives a graph instead, read values off the axes and quote them clearly, showing your read-off lines on the graph. Examiners award marks for the construction lines.
Part 3: The Traps That Cost the Most Marks
1. Forgetting to subtract background radiation
If a question gives a background count rate, subtract it from every reading before halving.
Measured 1000 counts/min, background 40 counts/min → corrected count rate = 960 counts/min. Then halve: 480, 240, 120.
This single step is worth a mark and is skipped constantly.
2. Confusing activity, count rate and number of nuclei
All three halve over one half-life, so the arithmetic is identical. But if the question asks for the number of undecayed nuclei, do not give the number that has decayed. After 2 half-lives, 25% remain and 75% have decayed.
3. Treating decay as predictable
Radioactive decay is random and spontaneous. It is not affected by temperature, pressure or chemical state. Expect a short answer question on this, and use those exact words.
4. Rounding too early
In multi-step half-life questions, carry full values through and round only at the end, to 3 significant figures.
A Quick Revision Routine
- Write out the alpha, beta and gamma table from memory in under a minute.
- Balance five decay equations a day for a week using past-paper isotopes.
- Do three half-life calculations: one forward, one backward, one graph-based.
- Write both half-life definitions and both randomness statements from memory.
Four short sessions and this topic is secured.
Our tutors are undergraduates from universities including Cambridge and NUS who sat these papers recently, so we teach the phrasing that actually earns marks, not just the theory.
Want to see how we break down a full Radioactivity past-paper question live? Start a free trial class with us on WhatsApp.