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 determine the half-life period of a radioactive isotope when the initial quantity is 3.0 g, given that the half-life period for 9.0 g of the same isotope is 10 hours.

### Step-by-Step Solution:

1. **Understand the Concept of Half-Life**:
The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. It is a characteristic property of the isotope and does not depend on the amount of substance present.

2. **Identify Given Information**:
- Half-life period (T₁/₂) of 9.0 g of the isotope = 10 hours.
- We need to find the half-life period for 3.0 g of the same isotope.

3. **Apply the Concept of Half-Life**:
Since the half-life of a radioactive isotope is independent of the quantity of the substance, the half-life period will remain the same regardless of whether we have 9.0 g or 3.0 g.

4. **Conclusion**:
Therefore, the half-life period of 3.0 g of the same substance is also 10 hours.

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

---