Assume initial concentration of the reactant = 1 M

After 100 second, concentration becomes of the reactant

= 1 $$ \times $$ $${{50} \over {100}}$$ = 0.5 M

After 200 second, concentration of the reactant becomes

= 1 $$ \times $$ $${{25} \over {100}}$$ = 0.25 M.

So, in first 100 second reactant concentration becomes half of initial and in the second 100 second concentration becomes 0.5 M to 0.25 M, which is also half of 0.5 M.

So, after each 100 second period, concentration of reactant becomes half of initial concentration.

So, 100 second is the half life period and it is independent of concentration of reactant. This is characteristic of first order reaction.