Derive the relationship between half life and rate constant for first order reaction.

Explanation

To derive the relationship between half-life (t₁/₂) and the rate constant (k) for a first-order reaction, we can follow these steps:

### Step 1: Understand the first-order reaction rate law
For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. The rate law can be expressed as:
\[ \text{Rate} = -\frac{d[A]}{dt} = k[A] \]
where:
- \([A]\) is the concentration of the reactant,
- \(k\) is the rate constant.
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