A sample has an activity of 960 Bq. Its half-life is 5.0 days. What is its activity after 20 days?
- Number of half-lives = 20 ÷ 5.0 = 4.
- Fraction remaining = (1/2)4 = 1/16.
- Activity = 960 ÷ 16 = 60 Bq (960 → 480 → 240 → 120 → 60).
Answer: 60 Bq
Radioactive decay
Physics · Nuclear and quantum physics. 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
Isotopes are nuclei with the same number of protons but different numbers of neutrons. Protons repel each other, but the strong nuclear force attracts all nucleons at very short range and holds the nucleus together.
A nucleus has less mass than its separate nucleons. This difference is the mass defect, and the equivalent energy is the binding energy. The higher the binding energy per nucleon, the more stable the nucleus. The curve peaks near iron.
Unstable nuclei decay by alpha, beta or gamma emission. Decay is random and spontaneous: we cannot say when one nucleus will decay, and heating or pressure does not change the rate. The half-life is the time for half the nuclei to decay.
Rules to remember
- Mass defect = total mass of the separate nucleons − mass of the nucleus; binding energy = mass defect × c² (E = Δmc²); 1 u = 931.5 MeV c−2
- Alpha decay: emits 42He, so A falls by 4 and Z falls by 2
- Beta-minus: neutron → proton + electron + antineutrino; A unchanged, Z rises by 1
- Beta-plus: proton → neutron + positron + neutrino; A unchanged, Z falls by 1
- Gamma: a photon is emitted; A and Z do not change
- Alpha: most ionizing, stopped by paper. Beta: stopped by a few mm of aluminium. Gamma: least ionizing, reduced by thick lead
- After n half-lives the fraction remaining is (1/2)n; subtract the background count before using half-life
Common mistake
Students mix up the fraction remaining and the fraction decayed. After three half-lives 1/8 remains, so 7/8 has decayed. Also remember that beta-minus comes with an antineutrino and beta-plus with a neutrino.
Worked example
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