If the stereochemistry about the double bond in `(A)` is trans, two diastereomers `(I)` and `(II)` exist as shown in Question.
Which statement is correct ?

Options

A. `(I)` is optically inactive due to the presence of plane of symmetry.
B. `(I)` is optically inactive due to the presence of centre of symmetry.
C. `(II)` is optically inactive due to the presence of plane of symmetry.
D. `(II)` is optically inactive due to the presence of centre of symmetry.

Answer

To solve the question regarding the stereochemistry of the diastereomers `(I)` and `(II)`, we need to analyze their optical activity based on their symmetry. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Structure of Diastereomers
- Given that the stereochemistry about the double bond in `(A)` is trans, we have two diastereomers `(I)` and `(II)`.
- Diastereomers are stereoisomers that are not mirror images of each other and can have different physical properties.

**Hint:** Identify the specific groups attached to the double bond in each diastereomer to analyze their spatial arrangement.

### Step 2: Analyze the Optical Activity
- Optical activity depends on the presence of chiral centers and the symmetry of the molecule.
- A molecule is optically active if it does not possess any element of symmetry (like a plane of symmetry or center of symmetry).

**Hint:** Look for any elements of symmetry in the structures of `(I)` and `(II)`.

### Step 3: Examine Diastereomer `(I)`
- In diastereomer `(I)`, check for symmetry. If there is no plane of symmetry or center of symmetry, it is optically active.

**Hint:** Draw the structure of `(I)` and look for any lines of symmetry.

### Step 4: Examine Diastereomer `(II)`
- In diastereomer `(II)`, it is noted that there is a center of symmetry. This means that the molecule is symmetrical and thus optically inactive.

**Hint:** Identify the position of substituents in `(II)` to confirm the presence of symmetry.

### Step 5: Evaluate the Statements
- Based on the analysis:
- Diastereomer `(I)` is optically active.
- Diastereomer `(II)` is optically inactive due to the presence of a center of symmetry.

**Hint:** Compare the findings with the statements provided in the question to determine which one is correct.

### Conclusion
- The correct statement is that diastereomer `(II)` is optically inactive due to the presence of a center of symmetry, while diastereomer `(I)` is optically active.

**Final Answer:** The correct statement is (D): Second is optically inactive due to the presence of a center of symmetry.