In one half- life time duration
activity of a sample reduced to half of its initial value.
total number of nuclei present are reduced to half of its initial value.
number of radioactive nuclei present is reduced to half of its initial value
mass of sample is reduced to half of its initial value
Out of these, correct statements are

Options

A. I and II
B. I and III
C. II and IV
D. II and III

Answer

To solve the question, we need to analyze the statements related to the concept of half-life in radioactive decay. Let's break down the statements one by one.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
- Half-life (denoted as \( t_{1/2} \)) is the time required for a quantity to reduce to half its initial value. In the context of radioactive decay, it refers to the time taken for half of the radioactive nuclei in a sample to decay.

2. **Analyzing the Statements**:
- **Statement 1**: "Activity of a sample reduced to half of its initial value."
- **Explanation**: The activity of a radioactive sample is directly proportional to the number of radioactive nuclei present. Since the number of nuclei reduces to half in one half-life, the activity also reduces to half.
- **Conclusion**: This statement is **correct**.

- **Statement 2**: "Total number of nuclei present are reduced to half of its initial value."
- **Explanation**: In one half-life, the total number of radioactive nuclei present in the sample does indeed reduce to half of its initial value.
- **Conclusion**: This statement is **correct**.

- **Statement 3**: "Number of radioactive nuclei present is reduced to half of its initial value."
- **Explanation**: This statement is essentially the same as the previous one, as it refers specifically to the radioactive nuclei. After one half-life, the number of radioactive nuclei is half of the initial amount.
- **Conclusion**: This statement is **correct**.

- **Statement 4**: "Mass of sample is reduced to half of its initial value."
- **Explanation**: The mass of the sample will also reduce to half because the mass is directly related to the number of radioactive nuclei present. Since the number of radioactive nuclei is halved, the mass will also be halved.
- **Conclusion**: This statement is **correct**.

3. **Final Conclusion**:
- All four statements are correct. Therefore, the correct statements are:
- Activity of a sample reduced to half of its initial value.
- Total number of nuclei present are reduced to half of its initial value.
- Number of radioactive nuclei present is reduced to half of its initial value.
- Mass of sample is reduced to half of its initial value.

### Summary of Correct Statements:
- All statements (1, 2, 3, and 4) are correct.