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. The metal that crystallises in b.c.c. 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 length of the unit cell in NaCl is 552 pm.
`(r_(Na)^(+)=95"pm",r_(Cl^(-))=181"pm")`

Answer

To determine which of the statements regarding the C-S-Cl crystal and its properties are correct, we will analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement 1:** The coordination number of each type of ion in the C-S-Cl crystal is 8.

- **Explanation:** The C-S-Cl crystal is said to form a body-centered cubic (BCC) structure. In a BCC structure, there is one atom at the center of the cube and eight atoms at the corners. Each corner atom is shared among eight unit cells. Therefore, the coordination number, which is the number of nearest neighbors surrounding an atom, is indeed 8 for both C-S and Cl ions.

**Conclusion:** This statement is correct.

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

- **Explanation:** It has been established that the coordination number for a BCC structure is 8, not 12. Coordination number 12 is characteristic of face-centered cubic (FCC) structures.

**Conclusion:** This statement is incorrect.

### Step 3: Analyze the Third Statement
**Statement 3:** A unit cell of an ionic crystal shares some of its ions with another type of unit cell.

- **Explanation:** In ionic crystals, unit cells often share ions with adjacent unit cells. For example, in BCC or FCC structures, corner atoms are shared between multiple unit cells, indicating that ions are indeed shared.

**Conclusion:** This statement is correct.

### Step 4: Analyze the Fourth Statement
**Statement 4:** NaCl has an edge length of 522 picometers, where R(Na⁺) is 95 pm and R(Cl⁻) is 181 pm.

- **Explanation:** NaCl forms a face-centered cubic (FCC) structure. The relationship between the edge length (a) and the ionic radii can be expressed as:
\[ \sqrt{2}a = R(Na^+) + R(Cl^-) = 95 + 181 = 276 \text{ pm} \]
Thus,
\[ a = \frac{276}{\sqrt{2}} \approx 195.6 \text{ pm} \]
This value is significantly less than 522 pm, indicating that the statement about the edge length is incorrect.

**Conclusion:** This statement is incorrect.

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

### Correct Statements
The correct statements are: **1 and 3.**

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