Half-life for certain radioactive element is `5 min`. Four nuclei of that element are observed at a certain instant of time. After `5` minutes
STATEMENT-I: It can be definitely said that two nuclei will be left undecayed.
STATEMENT-II: After half-life that is `5` minutes, half of totan nuclei will disintegrate. So, only two nuclei will be left undecayed.

Options

A. A is correct & R is correct expianation of A
B. Both are correct But R is not correct explanation of A
C. A is incorrect & R is correct
D. Both are incorrect

Explanation

To solve the question, we need to analyze the statements regarding the decay of radioactive nuclei over time, specifically focusing on the half-life concept.

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life of a radioactive element is the time required for half of the radioactive nuclei in a sample to decay. In this case, the half-life is given as 5 minutes.

2. **Initial Condition**: We start with 4 nuclei of the radioactive element.

3. **After 5 Minutes (First Half-Life)**:
- After one half-life (5 minutes), half of the initial nuclei will have decayed.
- Calculation:
\[ \text{Remaining nuclei} = \frac{4}{2} = 2 \]
- Thus, after 5 minutes, 2 nuclei will remain undecayed.

4. **Interpreting Statement-I**:
- Statement-I claims that "It can be definitely said that two nuclei will be left undecayed."
- This statement implies certainty about the outcome. However, radioactive decay is a probabilistic process. While it is likely that 2 nuclei will remain, we cannot say with absolute certainty that this will happen every time. Therefore, Statement-I is **incorrect**.

5. **Interpreting Statement-II**:
- Statement-II states that "After half-life that is 5 minutes, half of the total nuclei will disintegrate. So, only two nuclei will be left undecayed."
- This statement correctly describes the half-life process. After 5 minutes, we expect half of the initial nuclei (which is 2 out of 4) to remain. Therefore, Statement-II is **correct**.

6. **Conclusion**:
- Statement-I is incorrect because it uses the term "definitely," which does not apply to radioactive decay.
- Statement-II is correct as it accurately describes the expected outcome after one half-life.

### Final Answer:
- **Statement-I**: Incorrect
- **Statement-II**: Correct