Staements I: To determine the age of certain very old oragnic samples, dating of the sample with radioactive isotpes having larger half-life is a better choice than with radioactive isotopes having smaller half-lives.
Staements II: The activity of a radioactive sample having smaller half-life is negligibly small after a very long time and hence makes it next to impossible to get dtected.

Explanation

To solve the question, we need to analyze both statements provided in the question and determine their validity and relationship.

### Step 1: Analyze Statement I
Statement I claims that to determine the age of very old organic samples, using radioactive isotopes with larger half-lives is a better choice than using those with smaller half-lives.

- **Explanation**: Radioactive isotopes decay over time, and the half-life is the time required for half of the radioactive atoms in a sample to decay. For very old samples, isotopes with larger half-lives will still have a significant amount of the original isotope remaining, making it easier to measure and determine the age accurately. In contrast, isotopes with smaller half-lives will decay quickly, leaving very little of the original isotope after a long time, which makes it challenging to measure.

### Conclusion for Statement I:
- **True**: Larger half-lives are indeed better for dating very old samples.

### Step 2: Analyze Statement II
Statement II states that the activity of a radioactive sample with a smaller half-life becomes negligibly small after a very long time, making it nearly impossible to detect.

- **Explanation**: As time passes, radioactive isotopes with smaller half-lives decay rapidly. After a long duration, the remaining quantity of the isotope becomes very small, leading to a significantly reduced activity. This reduced activity makes it difficult to detect and measure the isotope, which in turn complicates the process of determining the age of the sample.

### Conclusion for Statement II:
- **True**: The activity of isotopes with smaller half-lives does become negligibly small over time.

### Step 3: Relationship Between Statements
Now we need to determine if Statement II provides a correct explanation for Statement I.

- **Explanation**: Statement II explains why Statement I is true. The reason larger half-lives are preferable for dating is precisely because smaller half-lives lead to negligible activity, making detection and age determination difficult.

### Final Conclusion:
- Both statements are correct, and Statement II is a valid explanation for Statement I.

### Final Answer:
- Both Statement I and Statement II are correct, and Statement II is the correct explanation of Statement I.

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