In which operations , the formula of NaCl remains same ?

Options

A. On passing one body-diagonal plane in unit cell and all the ions are removed touching body-diagonal plane
B. On passing one reactangular plane in unit cell and all the ions are removed touching rectangular plane
C. On passing tetrad axis in unit-cell and all the ions are removed touching the tetrad axis
D. On passing body-diagonal line in unit cell and all the ions are removed touching the body diagonal line

Answer

To determine in which operations the formula of NaCl remains the same, we need to analyze the given options step by step.

### Step-by-Step Solution:

1. **Understanding the Structure of NaCl**:
- NaCl (sodium chloride) has a face-centered cubic (FCC) structure. In this structure, each sodium ion (Na⁺) is surrounded by six chloride ions (Cl⁻) and vice versa. This arrangement is crucial for understanding how the formula remains unchanged during certain operations.

2. **Evaluating Option 1**:
- **Operation**: On passing one body diagonal plane in the unit cell and removing all ions touching the body diagonal plane.
- **Analysis**: When we remove ions along the body diagonal, the remaining ions still maintain the stoichiometry of NaCl. Therefore, the formula remains NaCl.
- **Conclusion**: This operation does not change the formula. **(Correct)**

3. **Evaluating Option 2**:
- **Operation**: On passing a rectangular plane in the unit cell and removing all ions touching the rectangular plane.
- **Analysis**: Similar to the first option, removing ions along a rectangular plane will not disrupt the overall ratio of Na⁺ to Cl⁻. Thus, the formula remains NaCl.
- **Conclusion**: This operation does not change the formula. **(Correct)**

4. **Evaluating Option 3**:
- **Operation**: On passing a tetrahedral axis in the unit cell and removing all ions touching the tetrahedral axis.
- **Analysis**: Removing ions along a tetrahedral axis also maintains the stoichiometric ratio of Na⁺ to Cl⁻. Hence, the formula remains NaCl.
- **Conclusion**: This operation does not change the formula. **(Correct)**

5. **Evaluating Option 4**:
- **Operation**: On passing the body diagonal line and removing all ions touching the body diagonal line.
- **Analysis**: This operation is slightly different from the first option. If we consider removing ions touching the body diagonal line itself, it may disrupt the balance of Na⁺ and Cl⁻ ions, potentially changing the formula.
- **Conclusion**: This operation may change the formula. **(Incorrect)**

### Final Answer:
The correct options where the formula of NaCl remains the same are **1, 2, and 3**.