To solve this problem, we need to understand the relationship between the order of a reaction and its half-life.$\newline$The half-life of a reaction is the time required for the concentration of a reactant to reduce to half of its initial value.$\newline$For different orders of reactions, the half-life behaves differently:$\newline$• Zero-order reaction: The half-life is directly proportional to the initial concentration.$\newline$• First-order reaction: The half-life is independent of the initial concentration.$\newline$• Second-order reaction: The half-life is inversely proportional to the initial concentration.$\newline$Given in the problem:$\newline$• When the initial concentration of a reactant is doubled, the half-life period is not affected.$\newline$This implies that the half-life is independent of the initial concentration, which is characteristic of a first-order reaction.$\newline$Therefore, the order of the reaction is first.$\newline$This corresponds to Option 1.