What is the correct relation between rate constant and half-life for zero order reaction

What is the correct relation between rate constant and half-life for zero order reaction
  1. $\mathrm{k}=[\mathrm{A}]_0 \times \mathrm{t}_{1 / 2}$
  2. $\mathrm{k}=\frac{2[\mathrm{~A}]_0}{\mathrm{t}_{1 / 2}}$
  3. $\mathrm{k}=\frac{[\mathrm{A}]_0}{\mathrm{t}_{1 / 2}}$
  4. $\mathrm{k}=\frac{[\mathrm{A}]_0}{2 \mathrm{t}_{1 / 2}}$

Solution

For zero order $\mathrm{rx}^{\mathrm{n}}$ $\begin{aligned} & \mathrm{x}=\mathrm{kt} \\ & \text { or } \frac{\left[\mathrm{A}_0\right]}{2}=\mathrm{k} \cdot \mathrm{t}_{1 / 2}\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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