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Learn4PH1Paper 1P · Paper 1 (core content)Radioactivity and particlesHalf-life, uses and safety
Radioactivity and particles · Subtopic 3 of 4

Half-Life, Uses and Safety

The half-life of an isotope is the time for half its nuclei to decay, so the activity halves every half-life. After nn half-lives, (12)n\left(\tfrac12\right)^n remains. Each use of radioactivity needs the right emission and the right half-life. Because ionising radiation damages cells, sources are handled with tongs, shielded and kept at a distance.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 30 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Define half-life and use it in calculations.
  • Read a half-life from a decay curve or table.
  • Explain the choice of isotope for each use, by emission and half-life.
  • Describe the dangers of ionising radiation and how to handle sources safely.
Pause and think

A sample's count rate halves every 1010 minutes. Will it ever reach exactly zero?

Section 2 of 14

Core idea

Start herePopcorn

You can't say which kernel will pop next, but you can say roughly how long until half have popped. Radioactive decay is the same: each nucleus is random, but a large sample halves at a steady, predictable rate.

The big idea

Half-life: time for half the nuclei (or the activity) to decay. After nn half-lives, (12)n(\frac12)^n remains.

1. The curve

Activity of a sample with half-life 2 hours
2468101002003004005006007008000time (hours)count rate (counts/min)halves every 2 h800400200100
Read the half-life from any starting point: the time to halve is always 2 hours.
A=A0(12)nA=A_0\left(\tfrac12\right)^n
where
A0A_0
starting activity.
nn
number of half-lives elapsed.
Worked example800 Bq, half-life 2 h

Activity after 2, 4, 6 h.

Goal
Values.
Strategy
Halve each 2 h.
  1. 800→400→200→100800\to400\to200\to100
    Three halvings.
  2. 100800=18\tfrac{100}{800}=\tfrac18
    Fraction after 6 h.
Answer400400, 200200, 100100 Bq.
✓ Check(12)3=18(\frac12)^3=\frac18 ✓.
Worked exampleFinding a half-life

640 to 40 counts/min in 20 days (background already subtracted).

Goal
Half-life.
Strategy
Count halvings.
  1. 640→320→160→80→40640\to320\to160\to80\to40
    Four halvings.
  2. 20÷4=5 days20\div4=5\text{ days}
    Each halving.
Answer55 days.
✓ Check640/16=40640/16=40 ✓.
Common misconceptionBackground count Subtract background before halving.
Pause and think

Why is a short half-life best for a medical tracer?

Summary

  • Halve repeatedly.
  • Correct for background.
Key words
Half-life
Time for activity to halve.
HistoryMarie Curie's notebooks. Marie Curie discovered polonium and radium and won two Nobel Prizes, but nobody then knew how dangerous radiation was. She died of radiation-induced illness in 19341934. Her notebooks are still so radioactive that they're kept in lead-lined boxes and readers must sign a waiver.
Fun factDating Ötzi the Iceman. Ötzi, a man found frozen in the Alps in 19911991, was first thought to be a recent mountaineer. Carbon-14 dating showed he died about 53005300 years ago, almost exactly one half-life of carbon-14.
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