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What does half-life mean, and how do we use it?

Half-life: the meaning of half-life, calculating activity after a number of half-lives, and the difference between contamination and irradiation.

A focused answer to AQA GCSE Physics 4.4.2, covering the meaning of half-life, how to calculate the remaining activity or number of nuclei after several half-lives, and the difference between radioactive contamination and irradiation.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Why decay is random but half-life is constant
What half-life means
Calculating with half-life
Contamination and irradiation
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What this dot point is asking

AQA wants you to define the half-life of a radioactive isotope, calculate the activity or number of undecayed nuclei after a whole number of half-lives, and distinguish radioactive contamination from irradiation. This sits in topic 4.4.2 of the AQA GCSE Physics (8463) specification and is examined on Paper 2 (combined trilogy candidates meet it on their Physics Paper 2 as well).

Why decay is random but half-life is constant

Radioactive decay is a random process at the level of a single nucleus. You cannot say when one particular nucleus will decay, and nothing you do (heating, cooling, chemical reaction, pressure) changes the chance of decay. Despite this randomness, a large sample contains so many billions of nuclei that the average behaviour is highly predictable. This is the same statistical idea as tossing a huge number of coins: any single coin is unpredictable, but you can be confident that close to half will land heads.

Because each nucleus has a fixed probability of decaying per second, the rate at which the sample loses nuclei (the activity) is proportional to how many undecayed nuclei are left. As the number of undecayed nuclei falls, the activity falls in step. This produces a curve that always takes the same time to halve, no matter where you start on it, and that constant time is the half-life.

What half-life means

Activity is measured in becquerels ( $Bq$ ), where one becquerel is one decay per second. A Geiger-Muller tube connected to a counter measures the count rate, which is proportional to the activity but is always a little lower because not every emission enters the tube. Examiners accept "count rate halves" or "activity halves" as equivalent to "number of nuclei halves".

Half-lives vary enormously between isotopes. Carbon-14, used in radiocarbon dating, has a half-life of about $5730$ years. Cobalt-60, used in some cancer treatments, has a half-life of about $5.3$ years. Iodine-131, used as a medical tracer, has a half-life of only $8$ days, which is useful because it does not stay radioactive in the body for long.

Calculating with half-life

To find the fraction that has decayed instead of the fraction remaining, subtract from one: after $n$ half-lives the fraction decayed is $1 - \left(\frac{1}{2}\right)^n$ . AQA often asks for the percentage decayed, so practise both directions.

Worked example: net decline as a ratio

A source has an initial activity of $1600\,Bq$ and a half-life of $20$ minutes. Find the activity after $1$ hour and express the decline as a ratio.

Step 1: Convert the total time into a number of half-lives

The key is to divide the total elapsed time by one half-life period. This tells you how many times the activity halves:

n = \dfrac{60\,\text{min}}{20\,\text{min}} = 3 \text{ half-lives}

Step 2: Halve the activity once for each half-life

Each half-life reduces the activity by half. Tracking it step by step makes the pattern clear:

1600\,Bq \xrightarrow{20\,\text{min}} 800\,Bq \xrightarrow{40\,\text{min}} 400\,Bq \xrightarrow{60\,\text{min}} 200\,Bq

Step 3: Express the fraction remaining using the half-life formula

The fraction of the original activity remaining after $n$ half-lives is $\left(\dfrac{1}{2}\right)^n$ . For $n = 3$ :

\left(\dfrac{1}{2}\right)^3 = \dfrac{1}{8}

This confirms the activity fell from $1600\,Bq$ to $1600 \times \dfrac{1}{8} = 200\,Bq$ .

Step 4: State the net decline as a ratio

The activity that has been lost is $1600 - 200 = 1400\,Bq$ . As a ratio of the original: $1400 : 1600 = 7 : 8$ of the original has decayed, leaving $1 : 8$ remaining.

Final answer: activity after $1$ hour $= 200\,Bq$ ; fraction remaining $= \dfrac{1}{8}$ ; net decline ratio $= 7 : 8$ .

Contamination and irradiation

The hazard depends on the type of radiation and on whether the source is inside or outside the body. Outside the body, gamma and beta are more hazardous because they can penetrate skin, while alpha is largely stopped by the outer dead layer of skin. Inside the body (contamination), alpha becomes the most dangerous because all its energy is deposited in a small region of living tissue, causing intense ionisation. This is why scientists handling radioactive sources use tongs, lead shielding, and protective clothing, and why peer review of studies on radiation risk matters: published conclusions are checked by other scientists before they are accepted.

Try this

Q1. Define the half-life of a radioactive isotope. [2 marks]

Cue. The time taken for the number of undecayed nuclei (or the activity) to halve.

Q2. A source has an activity of $640\,Bq$ and a half-life of $2$ hours. What is its activity after $6$ hours? [3 marks]

Cue. $6$ hours is $3$ half-lives: $640 \to 320 \to 160 \to 80\,Bq$ .

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20192 marksDefine what is meant by the half-life of a radioactive isotope.

Show worked answer →

A full-mark response states that the half-life is the time taken for the number of undecayed (radioactive) nuclei in a sample to halve, or equivalently the time for the activity (count rate) to halve. Markers award one mark for "time taken" and a second for "number of nuclei halves" or "activity halves". Saying "time for the source to decay" scores zero because the activity never reaches zero, it only halves repeatedly. The AO1 skill here is precise recall of the definition.

AQA 20214 marksA radioactive source has an initial activity of

7200\,\text{Bq}

and a half-life of

15

hours. Calculate the activity of the source after

60

hours, and calculate the net decline in activity as a fraction of the initial activity.

Show worked answer →

First find the number of half-lives: $n = 60 / 15 = 4$ (1 mark). The fraction of activity remaining is $\left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^4 = \frac{1}{16}$ (1 mark). So the activity after $60$ hours is $7200 \times \frac{1}{16} = 450\,\text{Bq}$ (1 mark). The net decline as a fraction of the initial activity is $1 - \frac{1}{16} = \frac{15}{16}$ , which is $0.9375$ or about $94\%$ (1 mark). Markers reward the half-life count, the correct fraction, the final activity, and the net-decline ratio. A common error is to divide $7200$ by $4$ instead of halving four times.

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Sources & how we know this

AQA GCSE Physics (8463) specification — AQA (2016)