The half-life period of reaction is the time needed for the reactant concentration to fall to one half of its initial value.
The rate equation for first order reaction is k=2.303tlog[A]0[A]t
When time t=t1/2= half life period, the initial concentration decreases from [A]0 to [A]02
k=2.303t1/2log[A]0[A]02
k=2.303t1/2log 2
k=0.693k
The half-life period for such reaction is independent of the initial concentrations of the reactants.