A first order reaction takes 40 min for `30%` decomposition. Calculate `t_(1//2)`.

Explanation

To solve the problem of calculating the half-life (t_(1/2)) of a first-order reaction given that it takes 40 minutes for 30% decomposition, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the initial and final concentrations**:
- Let the initial concentration (A0) be 100 units.
- Since 30% of the substance decomposes, the remaining concentration (A) after 40 minutes is:
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