Infographics / Nuclear Medicine

Exponential radioactive decay law

Two panels. Left: activity plotted against time on a linear scale falls exponentially, halving every half-life (A0, then half A0, then quarter A0), approaching but never reaching zero. Right: the same decay plotted on a semi-log (logarithmic activity) scale is a straight line with slope minus the decay constant. Captions state A of t equals A0 times e to the minus lambda t, equals A0 over 2 to the n after n half-lives, so equal time intervals give equal fractional decrease; activity equals lambda N and is measured in becquerels.

Radioactive decay: exponential activity on a linear scale versus a straight line on a semi-log scale Two panels. Left: activity plotted against time on a linear scale falls exponentially, halving every half-life (A0, then half A0, then quarter A0), approaching but never reaching zero. Right: the same decay plotted on a semi-log (logarithmic activity) scale is a straight line with slope minus the decay constant. Captions state A of t equals A0 times e to the minus lambda t, equals A0 over 2 to the n after n half-lives, so equal time intervals give equal fractional decrease; activity equals lambda N and is measured in becquerels. Radioactive decay is exponential: a straight line on a semi-log plot linear scale A₀ ½A₀ ¼A₀ T½ 2T½ 3T½ time (half-lives) approaches zero but never reaches it semi-log scale 10³ 10² 10¹ 10⁰ activity (log scale) time straight line confirms exponential decay, slope = −λ A(t) = A₀ e^(−λt) = A₀ / 2ⁿ after n half-lives — equal time intervals give equal fractional (%) decrease. Activity A = λN (∝ number of undecayed atoms); SI unit = becquerel (Bq = s⁻¹), not the sievert.
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