Chemistry / Unit 12 Chem 2526 worked example, 60 to 90 seconds
Half-Life: Exponential Decay Defined and Measured
The idea
Half-life (Chem 1672) is the time required for half of any sample's remaining nuclei to decay, independent of how much material is present, resting on first-order kinetics (Chem 1657); this entry extends that home definition by measuring a nuclide's half-life, tracking a sample's decay rate over time and fitting it to the same first-order relationship this course already uses for reaction kinetics.
In practice
Cobalt-60's half-life of 5.27 years means a sample retains 50% of its original activity after one half-life, 25% after two, and 12.5% after three, the same halving pattern regardless of the sample's starting size. This exponential pattern is what lets a measured decay rate be converted into a half-life value in the first place, using the same first-order rate law this course already applies to ordinary reaction kinetics.
Where people slip
A shorter half-life means faster decay, not a smaller amount of material remaining at any one moment — two samples of different total mass can share the identical half-life if they are the same nuclide.
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