If 9.0 g of a radioactive isotope has a half life period of 10 hrs. The half life period of 3.0 g of the same substance is:

Options

A. 2.5hrs
B. 5.0hrs
C. 10 hrs
D. 40 hrs

Answer

To solve the problem, we need to understand the concept of half-life in radioactive decay. The half-life of a radioactive isotope is the time required for half of the radioactive atoms in a sample to decay.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Mass of radioactive isotope = 9.0 g
- Half-life of 9.0 g = 10 hours

2. **Understand the Concept of Half-Life:**
- The half-life of a radioactive substance is a constant property of that substance and does not depend on the amount of the substance present.

3. **Determine the Half-Life for 3.0 g:**
- Since the half-life is independent of the initial amount of the substance, the half-life for any amount of the same radioactive isotope will remain the same.
- Therefore, the half-life of 3.0 g of the same radioactive isotope will also be 10 hours.

4. **Conclusion:**
- The half-life period of 3.0 g of the radioactive isotope is 10 hours.

### Final Answer:
The half-life period of 3.0 g of the same substance is **10 hours**.

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