Which of the following statement(s) is (are) correct

Options

A. The coordination number of each type of ion in CsCl crystal is 8.
B. A metal that crystallizes in bcc strcutre has a coordination number of 12
C. A unit cell of an ionic crystal shares some of its ions with other unit cells.
D. The length of the unit cell in NaCl is 352 pm `(r_(Na^(+))=95"pm",r_(Cl^(-))=181"pm")`

Explanation

To determine which of the statements regarding the solid state and ionic crystals are correct, let's analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement 1:** The coordination number of each type of ions in CsCl crystal is 8.

- **Explanation:** In the CsCl crystal structure, cesium ions (Cs⁺) are located at the body center of the cubic unit cell, while chloride ions (Cl⁻) occupy the corners of the cube. Each Cs⁺ ion is surrounded by 8 Cl⁻ ions, and each Cl⁻ ion is also surrounded by 8 Cs⁺ ions. Hence, the coordination number for both ions is indeed 8.

**Conclusion:** This statement is correct.

### Step 2: Analyze the second statement
**Statement 2:** A metal that crystallizes in the BCC structure has a coordination number of 12.

- **Explanation:** The body-centered cubic (BCC) structure consists of atoms at the corners of the cube and one atom at the center. In a BCC structure, each atom is surrounded by 8 other atoms, leading to a coordination number of 8, not 12.

**Conclusion:** This statement is incorrect.

### Step 3: Analyze the third statement
**Statement 3:** A unit cell of ionic crystals shares some of its ions with other unit cells.

- **Explanation:** In ionic crystals, the ions at the corners and faces of the unit cell are shared with adjacent unit cells. For example, a corner ion is shared among 8 unit cells, while a face-centered ion is shared between 2 unit cells. This sharing is a characteristic of crystalline structures.

**Conclusion:** This statement is correct.

### Step 4: Analyze the fourth statement
**Statement 4:** The length of the unit cell in NaCl is 552 picometers.

- **Explanation:** NaCl crystallizes in a face-centered cubic (FCC) structure. The relationship between the unit cell length (a) and the ionic radii (R) in NaCl is given by \( a = 2R \) (where R is the sum of the ionic radii of Na⁺ and Cl⁻). The ionic radii for Na⁺ and Cl⁻ are approximately 95 pm and 181 pm, respectively. Thus, the total \( R \) is \( 95 + 181 = 276 \) pm, leading to \( a = 2 \times 276 = 552 \) pm.

**Conclusion:** This statement is correct.

### Final Summary of Statements
1. **Correct**
2. **Incorrect**
3. **Correct**
4. **Correct**

### Correct Statements:
- The correct statements are 1, 3, and 4.