In a certain first order reaction ,half the reaction was decomposed in 500 seconds. How long will it be until one tenth is left ?

Explanation

To solve the problem, we need to determine the time it takes for a first-order reaction to reach a point where only one-tenth of the reactant remains. Given that the half-life (T_half) of the reaction is 500 seconds, we can use the properties of first-order kinetics to find the answer.

### Step-by-Step Solution:

1. **Understand the Concept of Half-Life in First-Order Reactions:**
For a first-order reaction, the half-life is constant and is given by the formula:
\[
T_{1/2} = \frac{0.693}{k}
...