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What is half-life, and how is it found from a decay curve?

The random nature of radioactive decay, activity, half-life, reading half-life from a decay curve, and applications such as dating and medicine.

A focused answer to WJEC GCSE Physics topic 2.8 on half-life, covering the random nature of radioactive decay, activity, the definition of half-life, how to read half-life from a decay curve, and applications such as carbon dating and medical tracers.

Generated by Claude Opus 4.89 min answer

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  1. What this topic is asking
  2. Random decay and activity
  3. Half-life
  4. Reading a decay curve and applications
  5. Try this

What this topic is asking

WJEC wants you to explain that radioactive decay is random, define activity and half-life, read half-life from a decay curve, and describe applications. This is topic 2.8 Half-life in Unit 2 of WJEC GCSE Physics (3420).

Random decay and activity

Because decay is random, measured count rates fluctuate, which is why experiments record many counts and subtract the background count rate before drawing conclusions. The randomness is like rolling many dice at once: you cannot say which die will show a six on the next roll, but with enough dice you can predict very accurately what fraction will, and that average behaviour is what half-life describes.

The activity of a sample falls over time for a simple reason: as more nuclei decay, fewer unstable nuclei are left to decay, so the number decaying each second steadily drops. This is why the decay curve is steep at the start, when there are many nuclei left, and flattens later, when only a few remain.

Half-life

Reading a decay curve and applications

Try this

Q1. A source has a count rate of 640 Bq640\,\text{Bq} and a half-life of 22 hours. Find the count rate after 66 hours. [3 marks]

  • Cue. 6/2=36/2 = 3 half-lives: 640β†’320β†’160β†’80 Bq640 \rightarrow 320 \rightarrow 160 \rightarrow 80\,\text{Bq}.

Q2. State what is meant by the half-life of a radioactive isotope. [1 mark]

  • Cue. The average time for half the unstable nuclei (or the activity) to decay to half its value.

Exam-style practice questions

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

WJEC 20193 marksA radioactive source has an activity of 800 Bq800\,\text{Bq} and a half-life of 55 hours. Calculate its activity after 1515 hours.
Show worked answer β†’

A topic 2.8 Calculate question. In 1515 hours there are 155=3\dfrac{15}{5} = 3 half-lives (1 mark). After each half-life the activity halves: 800β†’400β†’200β†’100800 \rightarrow 400 \rightarrow 200 \rightarrow 100 (1 mark). So after 1515 hours the activity is 100 Bq100\,\text{Bq} (1 mark). Markers reward the number of half-lives, the repeated halving and the final value. A common error is to divide by 33 instead of halving three times.

WJEC 20224 marksExplain how you could use a decay curve to find the half-life of a sample, and what is meant by the random nature of decay.
Show worked answer β†’

A topic 2.8 Explain question. From the decay curve, read the starting activity (or count) on the vertical axis, then find the time for it to fall to half that value (1 mark); this time is the half-life (1 mark). Checking that it falls to a quarter in twice that time confirms it (1 mark). Decay is random: you cannot predict which nucleus will decay or when, only the probability, so half-life is an average measure (1 mark). Markers reward reading half the value, the time taken, and the randomness. A common error is to read a single point rather than a halving.

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