Which of the following statements 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 structure 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 edge length of the unit cell in `NaCl` is `552` pm (`r_(Na^(o+)) = 95` pm,` r_(Cl^(o+)) = 181 pm`).

Explanation

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

### Step 1: Analyze the First Statement
**Statement 1:** The coordination number of each type of iron in CsCl structure is 8.

- In the CsCl (cesium chloride) structure, each Cl⁻ ion is surrounded by 8 Cs⁺ ions. This means that the coordination number for Cl⁻ is 8.
- Similarly, each Cs⁺ ion is surrounded by 8 Cl⁻ ions, confirming that the coordination number for Cs⁺ is also 8.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement 2:** In the BCC (Body-Centered Cubic) structure, a metal has a coordination number of 12.

- In a BCC structure, each atom is surrounded by 8 other atoms. The arrangement consists of one atom at each corner of the cube and one atom at the center.
- Therefore, the coordination number in a BCC structure is 8, not 12.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the Third Statement
**Statement 3:** The unit cell of the ionic crystal shares some of its ions with the other unit cell.

- In ionic crystals like NaCl, the unit cell does share ions with adjacent unit cells. For example, the Na⁺ and Cl⁻ ions at the edges and corners of the unit cell are shared with neighboring unit cells.
- This sharing is a characteristic of ionic crystals and is true for many crystal structures.

**Conclusion:** This statement is **correct**.

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

- To find the edge length (a) of the NaCl unit cell, we can use the formula:
\[ a = 2 \times (r_{cation} + r_{anion}) \]
- Given that the radius of Na⁺ (cation) is 95 picometers and the radius of Cl⁻ (anion) is 181 picometers, we calculate:
\[ a = 2 \times (95 + 181) = 2 \times 276 = 552 \text{ picometers} \]

**Conclusion:** This statement is **correct**.

### Final Summary of Statements
- **Statement 1:** Correct
- **Statement 2:** Incorrect
- **Statement 3:** Correct
- **Statement 4:** Correct

Thus, the correct statements are A, C, and D.