For a given reaction, the product of half life (t_1/2) and the square of initial concentration of the reactant is constant. Then the order of reaction is

We know that half life is related to concentration as:

$$\begin{gathered} {\mathrm{t}}_{\frac{1}{2}}=[\mathrm{A}{]}^{1-\mathrm{n}}\text{ where }\mathrm{n}\text{ is the order of the reaction } \\ \text{ Here }\mathrm{n}=2 \\ {\mathrm{t}}_{\frac{1}{2}}=[\mathrm{A}{]}^{1-2}=\frac{1}{\left[\mathrm{A}\right]} \\ \mathrm{For} \mathrm{n}=0, {\mathrm{t}}_{\frac{{\displaystyle 1}}{{\displaystyle 2}}}=[\mathrm{A}{]}^{1-0}=\left[\mathrm{A}\right] \\ \mathrm{If} {\mathrm{t}}_{\frac{{\displaystyle 1}}{{\displaystyle 2}}}\text{ is doubled, }[\mathrm{A}]\text{ is also doubled then the reaction is of zero order. } \end{gathered}$$