Which of the following statements is (are) correct ?

Options

A. The coordination number of fluoride ions in CaF_2 crystal is 4
B. A metal that crystallizes in bcc structure has a coordination number of 12
C. A unit cell of an bcc crystal shares some of its atoms with other unit cells
D. The length of the unit cell in NaCl is 552pm
`(r_(Na^(+))=90 "pm" , r_(Cl^(-))=186 "pm")`

Answer

To solve the problem, we will analyze each of the statements provided in the question regarding the solid state chemistry concepts.

### Step-by-Step Solution:

1. **Statement 1: Coordination number of the fluoride ion in CaF2 crystal is 4.**
- In the CaF2 crystal structure, calcium ions (Ca²⁺) occupy the face-centered cubic (FCC) lattice, while fluoride ions (F⁻) occupy the tetrahedral voids.
- Each tetrahedral void is surrounded by four fluoride ions, which gives the coordination number of the fluoride ion as 4.
- **Conclusion:** This statement is **correct**.

2. **Statement 2: A metal crystallizes in a BCC structure has a coordination number of 12.**
- In a body-centered cubic (BCC) structure, there are atoms at the corners and one atom at the body center.
- Each corner atom is shared among 8 unit cells, and the body-centered atom is not shared. The coordination number for a BCC structure is 8, not 12.
- **Conclusion:** This statement is **incorrect**.

3. **Statement 3: A unit cell of a BCC crystal shares some of its atoms with other unit cells.**
- In a BCC structure, the corner atoms are shared among 8 unit cells, and the body-centered atom is unique to that unit cell.
- Therefore, it is correct to say that a unit cell shares some of its atoms with other unit cells.
- **Conclusion:** This statement is **correct**.

4. **Statement 4: The length of the unit cell in NaCl is 552 picometers if the radius of cation is 90 picometers and the radius of anion is 186 picometers.**
- In NaCl, the sodium ions (Na⁺) occupy octahedral voids in a face-centered cubic (FCC) lattice formed by chloride ions (Cl⁻).
- The edge length (A) of the unit cell can be calculated as:
\[ A = R_{Na^+} + R_{Cl^-} + R_{Na^+} + R_{Cl^-} = 2R_{Na^+} + 2R_{Cl^-} \]
- Substituting the given values:
\[ A = 2(90 \text{ pm}) + 2(186 \text{ pm}) = 180 \text{ pm} + 372 \text{ pm} = 552 \text{ pm} \]
- **Conclusion:** This statement is **correct**.

### Final Conclusion:
The correct statements are:
- Statement 1: Correct
- Statement 2: Incorrect
- Statement 3: Correct
- Statement 4: Correct

Thus, the correct options are **1st, 3rd, and 4th**.

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