Assertion :- (A) the paking efficiency is maximum for the fcc struture .
Reason :- ( R) the coordination number is 2 in fcc structures.

Options

A. Assertion and reason both are correct statements and Reason is correct explantion for Assertion .
B. Asserton and Reason both are correct statement but Reason is not correct explanation for assertion .
C. Assertion is correct statement but reason is worng statement .
D. Assertion is Wrong statement but Reason is correct statement .

Explanation

To solve the question regarding the assertion and reason related to the packing efficiency of the FCC structure, we will follow these steps:

### Step 1: Understand the Assertion
The assertion states that the packing efficiency is maximum for the FCC (Face-Centered Cubic) structure.

### Step 2: Understand the Reason
The reason provided states that the coordination number is 2 in FCC structures. However, this is incorrect; the coordination number for FCC is actually 12.

### Step 3: Analyze the Packing Efficiency
- **Packing Efficiency**: This is defined as the fraction of volume occupied by the atoms in a unit cell compared to the total volume of the unit cell.
- For FCC, the packing efficiency can be calculated using the formula:
\[ \text{Packing Efficiency} = \frac{z \times \text{Volume of one atom}}{\text{Volume of the unit cell}} \times 100 \]
where \( z \) is the number of atoms per unit cell.

### Step 4: Calculate the Number of Atoms in FCC
- In an FCC unit cell:
- There are 8 atoms at the corners, each contributing \( \frac{1}{8} \) to the unit cell.
- There are 6 atoms at the face centers, each contributing \( \frac{1}{2} \) to the unit cell.

Thus, the total number of atoms \( z \) in an FCC unit cell is:
\[ z = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

### Step 5: Calculate the Packing Efficiency for FCC
- The volume of one atom (considering it as a sphere) is given by:
\[ \text{Volume of one atom} = \frac{4}{3} \pi r^3 \]
- The volume of the unit cell is \( a^3 \), where \( a \) is the edge length of the cube.

Using the relationship between the radius \( r \) and the edge length \( a \) in FCC, we find:
\[ 4r = \sqrt{2}a \implies r = \frac{\sqrt{2}}{4}a \]

Now substituting \( r \) back into the volume formula:
\[ \text{Volume of one atom} = \frac{4}{3} \pi \left(\frac{\sqrt{2}}{4}a\right)^3 = \frac{4}{3} \pi \frac{2\sqrt{2}}{64} a^3 = \frac{\pi \sqrt{2}}{48} a^3 \]

Now substituting into the packing efficiency formula:
\[ \text{Packing Efficiency} = \frac{4 \times \frac{4}{3} \pi r^3}{a^3} \times 100 \]

Calculating this gives a packing efficiency of approximately 74% for FCC, which is the highest among common crystal structures.

### Step 6: Conclusion
- The assertion is true: the packing efficiency is maximum for FCC structure.
- The reason is incorrect because the coordination number is 12, not 2.

### Final Answer
Both the assertion and reason are correct statements, but the reason does not correctly explain the assertion. Therefore, the correct conclusion is that the assertion is true, but the reason is false.