Half life of the first order reactions (t₁/₂)

Radioactive processes follow first order kinetics. The half life of a reaction is the time required for the reactant concentration to fall to one half of its initial value.

For a first order reaction the half life turns out to be a constant of the reaction: as section 6.5.4 derives, $t_{1/2} = 0.693/k$, which contains no concentration term at all. Whatever amount you start with, half of it is gone after one $t_{1/2}$, half of the remainder after the next $t_{1/2}$, and so on — the equal steps pictured in Fig. 6.2. This independence from the initial concentr …