For a first-order reaction, the half-life period is independent of

Solution :
$${t_{\frac{1}{2}}}\,\,{\text{of}}\,\,{n^{th}}\,\,{\text{order reaction}} \propto \frac{1}{{{a^{n - 1}}}}$$
where, $$a=$$  initial concentration of reactant
             $$n=$$  order of reaction
$$\therefore \,\,{t_{\frac{1}{2}}}$$   for first order reaction $$\left( {n = 1} \right)$$
$$\eqalign{ & {t_{\frac{1}{2}}} \propto \frac{1}{{{a^{1 - 1}}}} \cr & {\text{or}}\,\,\,{t_{\frac{1}{2}}} \propto \frac{1}{{{a^0}}}\,\,\,\,\left( {{a^0} = 1} \right) \cr} $$
So, for a first order reaction half-life is independent on initial concentration of reactants.