Atomic StructureHow It Works

How It Works: Why the Curve Is Exponential

Part of Half-Life · GCSE GCSE Physics revision

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.

Topic position

Section 6 of 13

Practice

15 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.

Keep building this topic

Read this section alongside the surrounding pages in Half-Life. That gives you the full topic sequence instead of a single isolated revision point.

Uses Based on Half-Life Key Definitions ⏳ Counting Down the Atoms Understanding Half-Life

Practice Questions for Half-Life

What is the definition of half-life?

A. The time taken for all of the radioactive nuclei to decay
B. The time taken for half of the radioactive nuclei in a sample to decay
C. The time taken for the activity of a sample to double
D. Half of the time for a nucleus to become stable

1 markfoundation

Explain what is meant by saying radioactive decay is 'random and spontaneous'.

2 marksstandard

Quick Recall Flashcards

Why is radioactive decay described as random?

Radioactive decay is random because we cannot predict when any individual nucleus will decay. We can only predict the probability of decay and the average behaviour of large numbers of nuclei.

What is half-life?

Half-life is the time taken for half the unstable nuclei in a radioactive sample to decay, or the time for the activity of a radioactive source to fall to half its original value.

15 questions on Half-Life — practise free

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Uses Based on Half-Life

Key Definitions