Formula for half- life of a zero order reaction is

For zero order reaction, if concentration of reactant is $\left[\mathrm{C}_0\right]$ at time t and $\frac{\left[\mathrm{C}_0\right]}{2}$ at time $\mathrm{t}_2$, then $$\begin{aligned} & \mathrm{k}=\frac{\left[\mathrm{C}_0\right]-\left[\frac{\mathrm{C}_0}{2}\right]}{\mathrm{t}_2-\mathrm{t}_1}=\frac{\left[\mathrm{C}_0\right]-\left[\frac{\mathrm{C}_0}{2}\right]}{\mathrm{t}_{1/2}} \\ \therefore \quad & \mathrm{t}_{1/2}=\frac{\left[\mathrm{C}_0\right]}{2 \mathrm{k}} \end{aligned}$$ Thus, $\mathrm{t}_{1/2}$ for zero order reaction is directly proportional to the initial concentration of the reactant.