If the half-life of a radioactive sample is 10 hours its mean life is

Options

A. 14.4 h
B. 7.2 h
C. 20 h
D. 6.93 h

Explanation

To find the mean life of a radioactive sample given its half-life, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The half-life (\( t_{1/2} \)) of the radioactive sample is given as 10 hours.

2. **Understand the Relationship**:
- The mean life (\( t_{mean} \)) of a radioactive sample is related to its half-life by the formula:
\[ t_{mean} = \frac{t_{1/2}}{\ln(2)} \]
- Here, \( \ln(2) \) is a constant approximately equal to 0.693.

3. **Substitute the Values**:
- Substitute \( t_{1/2} = 10 \) hours into the formula:
\[ t_{mean} = \frac{10 \text{ hours}}{\ln(2)} \]

4. **Calculate \( t_{mean} \)**:
- Using the value of \( \ln(2) \approx 0.693 \):
\[ t_{mean} = \frac{10 \text{ hours}}{0.693} \]

5. **Perform the Calculation**:
- Now, calculate the value:
\[ t_{mean} \approx \frac{10}{0.693} \approx 14.4 \text{ hours} \]

6. **Conclusion**:
- Therefore, the mean life of the radioactive sample is approximately **14.4 hours**.

### Final Answer:
The mean life of the radioactive sample is **14.4 hours**.

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