How It Works: Why the Curve Is Exponential
Part of Half-Life — GCSE Physics
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 13 exam-style questions and 23 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. 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.
Topic position
Section 6 of 13
Practice
13 questions
Recall
23 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.