The half life of `Co^58` is 72 days its average life is

Options

A. 103.9 days
B. 50 days
C. 200 days
D. 320 days

Answer

To find the average life (mean life) of the radioactive isotope \( Co^{58} \) given its half-life, we can use the relationship between half-life and average life.

### Step-by-Step Solution:

1. **Identify the Half-Life**:
The half-life \( T_{1/2} \) of \( Co^{58} \) is given as 72 days.

2. **Use the Formula for Average Life**:
The average life (mean life) \( \tau \) of a radioactive substance is related to its half-life by the formula:
\[ \tau = \frac{T_{1/2}}{\ln(2)} \]
where \( \ln(2) \) is approximately 0.693.

3. **Calculate the Average Life**:
Substitute the value of \( T_{1/2} \) into the formula:
\[ \tau = \frac{72 \text{ days}}{0.693} \]

4. **Perform the Calculation**:
\[ \tau \approx \frac{72}{0.693} \approx 103.9 \text{ days} \]

5. **Conclusion**:
The average life of \( Co^{58} \) is approximately 103.9 days.

### Final Answer:
The average life of \( Co^{58} \) is **103.9 days**.

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