Which of the following statements are correct

Options

A. The coordination number of each type of ion in CsCl crystal is 8
B. A metal that crystallises in bcc structure has a coordination number of 12
C. A unit cell of ionic crystal shares some of its ion with other unit cells
D. The length of the unit cell in NaCl is 552 pm. `(gamma_(Na) = 95 pm, gamma_(Cl^(-) = 181 pm)`

Answer

To solve the question regarding the correctness of the statements related to the solid state, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Analyzing Option 1**:
- The statement claims that the coordination number of each type of ion in cesium chloride (CsCl) is 8.
- In CsCl, each cesium ion (Cs⁺) is surrounded by 8 chloride ions (Cl⁻) and vice versa.
- Therefore, the coordination number for both ions in CsCl is indeed 8.
- **Conclusion**: This statement is **correct**.

2. **Analyzing Option 2**:
- The statement claims that a metal that crystallizes in a body-centered cubic (BCC) structure has a coordination number of 12.
- In a BCC structure, each atom is surrounded by 8 other atoms, not 12.
- Therefore, the coordination number for a BCC structure is 8.
- **Conclusion**: This statement is **incorrect**.

3. **Analyzing Option 3**:
- The statement claims that a unit cell of an ionic crystal shares some of its ions with other unit cells.
- This is true as ionic crystals consist of repeating units, and the ions at the edges and corners of the unit cell are shared with adjacent unit cells.
- **Conclusion**: This statement is **correct**.

4. **Analyzing Option 4**:
- The statement claims that the length of the unit cell of NaCl is 552 pm.
- The unit cell length can be calculated using the formula:
\[ a = R_{Na^+} + R_{Cl^-} \quad (where \, a \, is \, the \, edge \, length) \]
- Given the ionic radii: \( R_{Na^+} = 95 \, pm \) and \( R_{Cl^-} = 181 \, pm \), we calculate:
\[ a = R_{Na^+} + R_{Cl^-} = 95 \, pm + 181 \, pm = 276 \, pm \]
- However, since NaCl has a face-centered cubic (FCC) structure, the effective length will be \( 2 \times (R_{Na^+} + R_{Cl^-}) \) for the face diagonal, which gives:
\[ a = 2 \times 276 \, pm = 552 \, pm \]
- **Conclusion**: This statement is **correct**.

### Final Answer:
The correct statements are **Option 1, Option 3, and Option 4**.

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