Assertion `:(A): ` The average life of radioactive element is infinity.
Reason `(R):` As a radioactive element disintegrates, more of it is formed in nature by itself.

Options

A. If both `(A)` and `(R)` are correct , and `(R)` is the correct explanation of `(A)`
B. If both `(A)` and `(R)` are correct, but (R) is not the correct explanation of `(A)`
C. If `(A)` is correct, but `(R)` is incorrect.
D. If `(A)` is incorrect, but `(R)` is correct.

Explanation

To solve the question regarding the assertion and reason about radioactive elements, we will analyze both statements step by step.

### Step 1: Analyze the Assertion
**Assertion (A):** "The average life of a radioactive element is infinity."

- The average life (or mean life) of a radioactive element is defined as the average time it takes for half of the radioactive nuclei in a sample to decay.
- For certain radioactive elements, especially those with very long half-lives, the decay process can take an extremely long time, leading to the conclusion that the average life can be considered infinite.
- This is because, theoretically, a radioactive substance never completely decays; it just becomes less and less over time, approaching zero but never actually reaching it.

**Conclusion for Assertion:** The assertion is true.

### Step 2: Analyze the Reason
**Reason (R):** "As a radioactive element disintegrates, more of it is formed in nature by itself."

- This statement suggests that as a radioactive element decays, it somehow regenerates or produces more of itself in nature.
- In reality, radioactive elements do not regenerate themselves. Instead, they decay into different elements or isotopes through radioactive decay processes (e.g., alpha decay, beta decay).
- For example, Uranium-238 decays into Thorium-234, and this process continues through a series of decay steps until a stable isotope is formed.
- Therefore, the idea that a radioactive element forms more of itself as it disintegrates is incorrect.

**Conclusion for Reason:** The reason is false.

### Final Conclusion
- The assertion is true, while the reason is false. Thus, the correct answer to the question is that the assertion is correct, but the reason is incorrect.