The half life period of a reaction is inversely proportional to the square of the initial concentration of the reactant, then the order of reactions is

Options

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

Explanation

To determine the order of a reaction based on the given information about its half-life, we can follow these steps:

### Step 1: Understand the relationship given
The problem states that the half-life period (T_half) of a reaction is inversely proportional to the square of the initial concentration of the reactant (A). This can be mathematically expressed as:
\[ T_{1/2} \propto \frac{1}{[A]^2} \]

### Step 2: Express the relationship mathematically
From the proportionality, we can write:
\[ T_{1/2} = \frac{k}{[A]^2} \]
where k is a constant of proportionality.

### Step 3: Relate half-life to reaction order
For a reaction of order n, the half-life can be expressed as:
- For a zero-order reaction:
\[ T_{1/2} = \frac{[A]_0}{2k} \]
- For a first-order reaction:
\[ T_{1/2} = \frac{0.693}{k} \]
- For a second-order reaction:
\[ T_{1/2} = \frac{1}{k[A]_0} \]
- For a third-order reaction:
\[ T_{1/2} = \frac{2}{k[A]_0^2} \]

### Step 4: Compare the expressions
We know from the problem that:
\[ T_{1/2} \propto \frac{1}{[A]^2} \]
This matches the expression for a third-order reaction:
\[ T_{1/2} = \frac{2}{k[A]^2} \]

### Step 5: Determine the order of the reaction
From the comparison, we can conclude that the order of the reaction is 3 (third-order), as it is the only case where the half-life is inversely proportional to the square of the initial concentration.

### Conclusion
Thus, the order of the reaction is **3**.

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