The half life of radioactive sodium is 15 hours its disintegration constant is

Options

A. `0.0462 h^(-1)`
B. `0.0642 h^(-1)`
C. `0.0462 s^(-1)`
D. `0.0462 "min"^(-1)`

Explanation

To find the disintegration constant (k) for radioactive sodium given its half-life, we can use the formula for the half-life of a first-order reaction:

### Step-by-Step Solution:

1. **Understand the relationship between half-life and disintegration constant**:
For a first-order reaction, the half-life (t₁/₂) is related to the disintegration constant (k) by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]

2. **Rearrange the formula to solve for k**:
To find k, we can rearrange the formula:
\[ k = \frac{0.693}{t_{1/2}} \]

3. **Substitute the given half-life**:
We know the half-life of radioactive sodium is 15 hours. We will substitute this value into the equation:
\[ k = \frac{0.693}{15 \text{ hours}} \]

4. **Calculate k**:
Now, perform the calculation:
\[ k = \frac{0.693}{15} \approx 0.0462 \text{ hours}^{-1} \]

5. **Conclusion**:
The disintegration constant (k) for radioactive sodium is approximately:
\[ k \approx 0.0462 \text{ hours}^{-1} \]