Assertion : For a first order reaction,`t_(1//2)` is indepent of rate constant.
Reason : For a first reaction `t_(1//2) prop [R]_(0)`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason related to first-order reactions, we will analyze both statements step by step.

### Step 1: Understanding the Assertion
The assertion states that for a first-order reaction, the half-life (\(t_{1/2}\)) is independent of the rate constant.

**Analysis**:
For a first-order reaction, the half-life is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \(k\) is the rate constant. This indicates that the half-life is inversely proportional to the rate constant \(k\). Therefore, as the rate constant changes, the half-life will also change.

**Conclusion**: The assertion is **false**.

### Step 2: Understanding the Reason
The reason states that for a first-order reaction, \(t_{1/2}\) is proportional to the initial concentration \([R]_0\).

**Analysis**:
For a first-order reaction, the half-life is independent of the initial concentration. The half-life remains constant regardless of the concentration of the reactant. The formula for half-life does not include the initial concentration, confirming that it does not depend on \([R]_0\).

**Conclusion**: The reason is also **false**.

### Final Conclusion
Both the assertion and the reason are false.

### Summary
- Assertion: False (Half-life for a first-order reaction is dependent on the rate constant).
- Reason: False (Half-life for a first-order reaction is independent of initial concentration).