GCSE Combined Science (AQA)

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Half-Life Calculations

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Atomic structure Atoms and nuclear radiation

Half-Life Calculations

2:49 Half-Life
Spec 4.4.2.3
Previous Measuring Half-Life Next Contamination
  • Determine the ratio of nuclei left in a sample using the number of half-lives passed.
  • Half-life is the time for the number of nuclei or activity to halve.
  • Proportion of nuclei remaining is found by halving the number of nuclei after each half-life.
  • Example proportions:
  • After 1 half-life: 1/2 remain
  • After 2 half-lives: 1/4 remain
  • After 3 half-lives: 1/8 remain
  • After 4 half-lives: 1/16 remain
  • After 5 half-lives: 1/32 remain
  • This proportion is consistent for any sample size.
  • Example: 72 gallium nuclei with a half-life of 14 hours.
  • Calculate ratio after 84 hours.
  • Step 1: Calculate number of half-lives (84 hours / 14 hours = 6 half-lives).
  • Step 2: Multiply half by itself 6 times (1/64 remain).
  • Example: Carbon 14 isotope decay.
  • Half-life of carbon 14 is 5,700 years.
  • Calculate age of a bone sample with carbon 14 activity 1/8 of a living bone.
  • Step 1: Calculate number of half-lives (1/8 = 3 half-lives).
  • Step 2: Calculate age (3 half-lives x 5,700 years = 17,100 years).

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