The decay curve is exponential rather than linear because the number of decays per second (activity) depends on how many radioactive nuclei are still present. More nuclei → more decays per second. As nuclei decay and the total number falls, the rate of decay falls proportionally.
Mathematically: Activity = decay constant × number of nuclei present (A = λN). As N decreases, A decreases at exactly the same rate. This means the same fraction (half) decays in each equal time interval — the definition of exponential decay.
This is why the curve flattens over time but never reaches zero. Even after 10 half-lives, you still have (½)¹⁰ ≈ 0.1% of the original material — a tiny but measurable amount for a large initial sample.
This how it works covers How It Works: Why the Curve Is Exponential within Half-Life for GCSE Physics. Revise Half-Life in Atomic Structure for GCSE Physics with 15 exam-style questions and 23 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 6 of 13 in this topic. Use this how it works to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Half-Life
What is the definition of half-life?
Explain what is meant by saying radioactive decay is 'random and spontaneous'.