If `8.0 g` of radioactive isotope has a half life of 10 hours, the half life of `2.0 g` of the same substance is

Options

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

Explanation

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. Importantly, the half-life is a characteristic property of the isotope and does not depend on the amount of the substance present.

### Step-by-step Solution:

1. **Identify the Given Information**:
- We have 8.0 g of a radioactive isotope with a half-life of 10 hours.

2. **Understand the Concept of Half-Life**:
- The half-life of a substance is the time it takes for half of the radioactive atoms to decay. This means that after one half-life, 50% of the original amount remains.

3. **Recognize the Independence of Half-Life from Quantity**:
- The half-life of a radioactive isotope is independent of the initial amount of the substance. This means that whether we have 8.0 g, 2.0 g, or any other amount, the half-life remains the same.

4. **Conclusion**:
- Since the half-life of the isotope is given as 10 hours for 8.0 g, it will also be 10 hours for 2.0 g of the same substance.

5. **Final Answer**:
- Therefore, the half-life of 2.0 g of the same radioactive isotope is **10 hours**.