Assertion (A) : In sodium chloride crystal, the coordination number of `Na^(o+)` IS `6`.
Reason (R ) : The sodium atom is smaller than chloring atom.
a.If both `(A)` and `(R)` are correct, and `(R)` is the correct explanation of `(A)`
b.If both `(A)` and `(R)` are correct, but `(R)` is not the correct explanation of `(A)`
c.If `(A)` is correct, but `(R)` is incorrect.
d.If both `(A)` is incorrect, but `(R)` is correct.

Options

A. If both `(A)` and `(R)` are correct, and `(R)` is the correct explanation of `(A)`
B. If both `(A)` and `(R)` are correct, but `(R)` is not the correct explanation of `(A)`
C. If `(A)` is correct, but `(R)` is incorrect.
D. If both `(A)` is incorrect, but `(R)` is correct.

Answer

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion (A):** In sodium chloride crystal, the coordination number of `Na^(+1)` is `6`.

**Reason (R):** The sodium atom is smaller than the chlorine atom.

### Step-by-Step Solution:

1. **Understanding Coordination Number:**
- The coordination number of an ion in a crystal lattice is defined as the number of nearest neighbor ions surrounding it. In the case of sodium chloride (NaCl), we need to determine how many chloride ions surround a sodium ion.

2. **Structure of Sodium Chloride:**
- Sodium chloride crystallizes in a face-centered cubic (FCC) lattice structure. In this structure, the sodium ions (Na+) occupy the edge centers, while the chloride ions (Cl-) occupy the face centers and corners of the cube.

3. **Counting Nearest Neighbors:**
- For a sodium ion located at the center of the cube, it is surrounded by six chloride ions. These chloride ions are located at the face centers of the cube, which are the nearest neighbors to the sodium ion. Therefore, the coordination number of Na+ in NaCl is indeed 6.

4. **Evaluating the Assertion:**
- Since we have confirmed that the coordination number of Na+ in NaCl is 6, the assertion (A) is correct.

5. **Evaluating the Reason:**
- The reason states that the sodium atom is smaller than the chlorine atom. This statement is also true; sodium (atomic number 11) has a smaller atomic radius than chlorine (atomic number 17). However, the size of the sodium atom does not directly explain why the coordination number is 6. The coordination number is determined by the arrangement of ions in the crystal lattice, not solely by the size of the ions.

6. **Conclusion:**
- Both the assertion (A) and the reason (R) are correct, but the reason does not provide a correct explanation for the assertion. Therefore, the correct answer is option (b): If both (A) and (R) are correct, but (R) is not the correct explanation of (A).