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.
⚙️ How It Works: Why the Curve Is Exponential
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.
Practice questions for Half-Life
What is the definition of half-life?
Explain what is meant by saying radioactive decay is 'random and spontaneous'.