The half life of 2g sample of radioactive nuclide 'X' is 15 min. The half life time of 1g sample of X is

Options

A. 7.5 min
B. 15 min
C. 22.5 min
D. 30 min

Answer

To solve the problem, we need to understand the concept of half-life in radioactive decay. The half-life of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay.

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life (T₁/₂) of a radioactive substance is the time taken for half of the substance to decay. It is a constant for a given nuclide and does not depend on the amount of substance present.

2. **Given Data**: We are given that the half-life of a 2g sample of radioactive nuclide 'X' is 15 minutes.

3. **Half-Life Independence**: Since the half-life of a radioactive substance is independent of the amount of substance, the half-life for any sample size remains the same.

4. **Calculating Half-Life for 1g Sample**: Therefore, the half-life for a 1g sample of nuclide 'X' is the same as that for a 2g sample.

5. **Conclusion**: Thus, the half-life of a 1g sample of radioactive nuclide 'X' is also 15 minutes.

### Final Answer:
The half-life time of a 1g sample of X is **15 minutes**.

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