A source has an activity of 960 Bq and a half-life of 5 days. What is its activity after 20 days?
- Number of half-lives = 20 ÷ 5 = 4.
- Halve four times: 960 → 480 → 240 → 120 → 60.
- Check: 960 × (½)4 = 960 ÷ 16 = 60.
Answer: 60 Bq
Radioactive decay, half-life and contamination
Physics · Atomic structure. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Some nuclei are unstable. They become more stable by giving out radiation: an alpha particle (a helium nucleus), a beta particle (a fast electron from the nucleus), a gamma ray (an electromagnetic wave) or a neutron. Decay is random. You cannot say which nucleus will decay next, or when.
Activity is the number of decays per second, measured in becquerels (Bq). The half-life is the time taken for the number of undecayed nuclei, or the activity, to fall to half.
Irradiation means being exposed to radiation from a source outside you; the object does not become radioactive. Contamination means radioactive atoms are on or in the object, so it keeps being exposed.
Rules to remember
- Alpha: most ionising, least penetrating; stopped by paper or a few centimetres of air.
- Beta: stopped by a few millimetres of aluminium; range in air about a metre.
- Gamma: least ionising, most penetrating; reduced by thick lead or concrete.
- Alpha decay: mass number falls by 4, atomic number falls by 2.
- Beta decay: mass number stays the same, atomic number rises by 1 (a neutron becomes a proton).
- Gamma emission: no change to the mass or the charge of the nucleus.
- After n half-lives the fraction remaining is (½)n: ½, ¼, ⅛, 1/16 ...
Common mistake
Students divide by the number of half-lives instead of halving that many times. After 3 half-lives one eighth remains, not one third. Also subtract the background count before halving a measured count-rate.
Worked example
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