Half`-`life of a radioactive disintegration `(A rarr B)` having rate constat `231s^(-1)` is

Options

A. `3.0 xx 10^(-2)s`
B. `3xx10^(-3)s`
C. `3.3xx10^(-2)s`
D. `3.3xx10^(-3)s`

Explanation

To find the half-life of a radioactive disintegration reaction \( A \rightarrow B \) with a given rate constant, we can follow these steps:

### Step 1: Understand the relationship between half-life and rate constant
For a first-order reaction, the relationship between the half-life (\( t_{1/2} \)) and the rate constant (\( k \)) is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]

### Step 2: Identify the rate constant
From the problem, we know that the rate constant \( k \) is given as:
\[ k = 231 \, \text{s}^{-1} \]

### Step 3: Substitute the value of \( k \) into the half-life formula
Now, we can substitute the value of \( k \) into the half-life formula:
\[ t_{1/2} = \frac{0.693}{231} \]

### Step 4: Calculate the half-life
Now, we perform the calculation:
\[ t_{1/2} = \frac{0.693}{231} \approx 0.003 \, \text{s} \]

### Step 5: Express the answer in scientific notation
The half-life can also be expressed in scientific notation:
\[ t_{1/2} \approx 3 \times 10^{-3} \, \text{s} \]

### Final Answer
Thus, the half-life of the radioactive disintegration \( A \rightarrow B \) is approximately:
\[ t_{1/2} \approx 3 \times 10^{-3} \, \text{s} \]

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