Which of the following statement(s) is incorrect?

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 length of the unit cell in NaCl is 552 pm `(r_(Na^+)=95"pm",r_(Cr^-)=181"pm")`

Answer

To determine which statement is incorrect regarding the solid state and crystal structures, we will analyze each statement one by one.

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

- **Explanation:** CsCl (cesium chloride) has a body-centered cubic (BCC) structure. In a BCC structure, each ion is surrounded by 8 nearest neighbors. Therefore, this statement is **correct**.

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

- **Explanation:** In a BCC structure, the coordination number is actually 8, not 12. The coordination number of 12 is characteristic of face-centered cubic (FCC) structures. Therefore, this statement is **incorrect**.

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

- **Explanation:** This statement is true. In ionic crystals, ions at the corners of the unit cell are shared among adjacent unit cells. For example, an ion located at a corner of a cube is shared by 8 adjacent unit cells. Hence, this statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** "The length of the unit cell in NaCl is calculated using the formula R + cation size + anion size = 2 times the side length."

- **Explanation:** This statement is also correct. For NaCl, the relationship between the ionic radii and the unit cell length is accurately described by the formula. The calculated length of the unit cell is consistent with the known values for NaCl. Therefore, this statement is **correct**.

### Conclusion
After analyzing all the statements, we find that the **incorrect statement is the second one**: "A metal crystallizes in BCC structure has a coordination number of 12."

### Final Answer
The incorrect statement is: **Option B**.

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