Infographics / Nuclear Medicine

Physical, biological & effective half-life

An exponential decay curve of activity against time measured in half-lives. Activity falls to 50% after one half-life, 25% after two, and 12.5% after three, illustrating that activity halves each successive half-life. Formulae shown: N equals N-zero times e to the minus lambda t, and half-life equals 0.693 divided by lambda. A note gives the effective half-life for a radiopharmaceutical, one over T-eff equals one over T-phys plus one over T-bio, so T-eff is shorter than either.

Radioactive decay curve showing half-life An exponential decay curve of activity against time measured in half-lives. Activity falls to 50% after one half-life, 25% after two, and 12.5% after three, illustrating that activity halves each successive half-life. Formulae shown: N equals N-zero times e to the minus lambda t, and half-life equals 0.693 divided by lambda. A note gives the effective half-life for a radiopharmaceutical, one over T-eff equals one over T-phys plus one over T-bio, so T-eff is shorter than either. Radioactive decay: activity halves each successive half-life activity (% of initial) time (in half-lives) 0 T½ 2 T½ 3 T½ 4 T½ 100% 50% 25% 12.5% N = N₀ e^(−λt) half-life T½ = 0.693 / λ = ln2 / λ each T½ the activity falls by ×½ Effective half-life of a radiopharmaceutical 1/T_eff = 1/T_phys + 1/T_bio → T_eff is shorter than both T_phys and T_bio e.g. T_phys = 6 h and T_bio = 6 h give T_eff = 3 h
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