In a first order reaction `A to B`, if k is rate constant and initial concentration o f the reactant A is 0.5 M then the half-life is

Options

A. `0.693/(0.5 K)`
B. `(log 2)/k`
C. `(log 2)/(ksqrt(0.5))`
D. `(ln 2)/k`

Explanation

To find the half-life of a first-order reaction where the initial concentration of reactant A is 0.5 M and the rate constant is k, we can follow these steps:

### Step 1: Understand the formula for half-life in a first-order reaction
The half-life (t₁/₂) of a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the rate constant.

### Step 2: Identify the given values
From the problem statement, we know:
- The reaction is first-order.
- The initial concentration of A is 0.5 M.
- The rate constant \( k \) is provided (though its numerical value is not specified in the question).

### Step 3: Substitute the values into the half-life formula
Since we do not have a specific value for \( k \), we will express the half-life in terms of \( k \):
\[ t_{1/2} = \frac{0.693}{k} \]

### Step 4: Conclusion
The half-life of the reaction is dependent on the rate constant \( k \). Therefore, the final expression for the half-life of the first-order reaction A to B is:
\[ t_{1/2} = \frac{0.693}{k} \]