The half`-` life periods of four isotopes are give below `:`
`(i) 7.6 years` , ` ii. 4000 years`
`iii. 6000 years`,`iv. 3.2xx10^(5) years`
Which of the above isotope is most stable ?

Options

A. `iv.`
B. `iii.`
C. `ii.`
D. `i.`

Explanation

To determine which isotope is the most stable among the given options based on their half-lives, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Half-Life**:
- The half-life of a radioactive isotope is the time required for half of the isotope to decay. A longer half-life indicates that the isotope decays more slowly, which suggests greater stability.

2. **List the Given Half-Lives**:
- (i) 7.6 years
- (ii) 4000 years
- (iii) 6000 years
- (iv) 3.2 × 10^5 years (which is 320,000 years)

3. **Compare the Half-Lives**:
- Now, we need to compare the half-lives to determine which is the longest:
- 7.6 years
- 4000 years
- 6000 years
- 320,000 years

4. **Identify the Longest Half-Life**:
- Among the values, 320,000 years is the largest. Therefore, the isotope with a half-life of 3.2 × 10^5 years is the most stable.

5. **Conclusion**:
- The isotope with the highest stability is the one with the longest half-life, which is the fourth option: 3.2 × 10^5 years.

### Final Answer:
The most stable isotope is the one with a half-life of **3.2 × 10^5 years**.

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