For a given reaction, the half-life period was found to be directly proportional to the initial concentration of the reactant. The order of reaction is

Options

A. 0
B. 1
C. 2
D. 3

Explanation

To determine the order of the reaction based on the relationship between the half-life period (T_half) and the initial concentration of the reactant (A_0), we can analyze the mathematical relationship that defines this connection.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The half-life period (T_half) of a reaction is related to the initial concentration (A_0) and the order of the reaction (n) by the formula:
\[ T_{1/2} \propto A_0^{(1-n)} \]
This means that the half-life is directly proportional to the initial concentration raised to the power of (1-n).

2. **Analyzing Different Orders**:
We will analyze the relationship for different orders of reactions (0, 1, 2, and 3) to find out which order satisfies the condition that T_half is directly proportional to A_0.

- **Zero Order (n = 0)**:
\[ T_{1/2} \propto A_0^{(1-0)} = A_0^1 \]
Here, T_half is directly proportional to A_0.

- **First Order (n = 1)**:
\[ T_{1/2} \propto A_0^{(1-1)} = A_0^0 \]
Here, T_half is independent of A_0.

- **Second Order (n = 2)**:
\[ T_{1/2} \propto A_0^{(1-2)} = A_0^{-1} \]
Here, T_half is inversely proportional to A_0.

- **Third Order (n = 3)**:
\[ T_{1/2} \propto A_0^{(1-3)} = A_0^{-2} \]
Here, T_half is inversely proportional to the square of A_0.

3. **Conclusion**:
From the analysis, we can see that the only order of reaction where the half-life period is directly proportional to the initial concentration of the reactant is for a **zero-order reaction**.

### Final Answer:
The order of the reaction is **0** (zero order).