If 2.0g of a radioactive isotope has a half-life of 20 hr, the half-life of 0.5 g of the same substance is

Options

A. 20 hr
B. 80 hr
C. 5 hr
D. 10 hr

Explanation

To solve the problem, we need to understand the concept of half-life in radioactive decay. The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. Importantly, the half-life of a radioactive isotope is a constant value and does not depend on the amount of substance present.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have 2.0 g of a radioactive isotope.
- The half-life (T_half) of this isotope is 20 hours.

2. **Understand the Concept of Half-Life:**
- The half-life of a radioactive isotope is a characteristic property of that isotope. It remains constant regardless of the quantity of the substance.

3. **Apply the Concept:**
- Since the half-life is a constant for a given isotope, the half-life for any amount of that isotope will be the same. Therefore, whether we have 2.0 g or 0.5 g of the same isotope, the half-life remains unchanged.

4. **Conclusion:**
- The half-life of 0.5 g of the same radioactive substance is also 20 hours.

### Final Answer:
The half-life of 0.5 g of the same radioactive isotope is **20 hours**.

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