Not given in the exam, recall it.
What it is for
Radioactive decay (half-life) is used in Nuclear Physics (SPM Physics Form 5). Keep the SI units in every line of working. Nuclear Physics
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| N | quantity remaining (no unit) | , |
| N₀ | initial quantity (no unit) | , |
| t | elapsed time | s |
| T½ | half-life | s |
| n | number of half-lives (= t / T½) | , |
Rearrangements
n = t / T½ (number of half-lives)N / N₀ = (½)ⁿ
Worked example
Common trap
Understanding Radioactive decay (half-life)
The decay law N = N₀ (½)ⁿ tells you how much of a radioactive sample is left after a time. N is the quantity remaining and N₀ the initial quantity; both are counts (number of nuclei, mass, or activity) and share the same unit. t is the elapsed time and T½ the half-life, both in the same time unit (s, minutes, hours, days or years).
The quantities relate because each half-life halves whatever is left, so the fraction remaining is (½) raised to the number of half-lives, t / T½.
To use it, first find the number of half-lives = t / T½. Then N / N₀ = (½)ⁿ gives the remaining fraction, which you multiply by N₀.
A worked example, step by step
A radioactive sample has an initial mass N₀ = 80 g and a half-life T½ = 2 years. Find the mass remaining after t = 6 years.
First count the half-lives:
number of half-lives = t / T½ = 6 years / 2 years = 3.
Each half-life halves the mass, so:
N = N₀ (½)³ = 80 g × (1/8) = 10 g.
You can check by halving in steps: 80 g → 40 g (2 yr) → 20 g (4 yr) → 10 g (6 yr), which agrees. The mass remaining is 10 g.
Common mistakes and how this is tested
The main trap is using different time units for t and T½, for example minutes with hours; convert them to match first. A second error is halving the wrong number of times, so always compute t / T½ before halving.
A third is subtracting a fixed amount each time instead of halving, since decay is not linear.
Under calculate, show the number of half-lives and each halving step to reach the remaining amount. Under define, state that half-life is the time taken for half of the radioactive nuclei to decay.
Under explain, you may be asked why half-life is constant regardless of the starting amount, or how it is used to date old materials.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)