Symmetry Elements and Optical Activity of Chiral Dichloro Compound

To determine the correct statements about the given molecule, let us analyze its stereochemistry and symmetry elements:

1. Identification of Stereocenters and Stereoisomer:
   The molecule shown is 2,3-dichlorobutane, which has two stereocenters (C2 and C3), each attached to four different groups: $-\text{CH}_3$, $-\text{H}$, $-\text{Cl}$, and $-\text{CH(Cl)CH}_3$.

   Determining the absolute configuration of each chiral center:

   • For a meso isomer of 2,3-dichlorobutane, the configuration is $(2R, 3S)$, which possesses either an internal plane of symmetry ($\sigma$) in the eclipsed conformation or an inversion center ($i$) in the anti-staggered conformation, making it achiral (optically inactive).
   • For the pair of enantiomers, the configurations are $(2R, 3R)$ and $(2S, 3S)$. These enantiomers do not possess any plane of symmetry ($\sigma$) or center of inversion ($i$) in any conformation. Instead, they possess a two-fold axis of rotation ($C_2$).

2. Symmetry Elements in the Given Conformation:

   • Axis of Symmetry ($C_2$): A $180^\circ$ rotation about an axis perpendicular to the central $\text{C}-\text{C}$ bond passing through its midpoint interchanges the two identical halves of the molecule ($-\text{CH}_3 \leftrightarrow -\text{CH}_3$, $-\text{Cl} \leftrightarrow -\text{Cl}$, and $-\text{H} \leftrightarrow -\text{H}$). Thus, the molecule possesses a $C_2$ axis of symmetry.
   • Plane of Symmetry ($\sigma$): Reflection across any plane does not yield a superimposable image due to the relative spatial arrangements of the $-\text{Cl}$, $-\text{H}$, and $-\text{CH}_3$ groups.
   • Centre of Symmetry ($i$): Inversion through the midpoint of the central $\text{C}-\text{C}$ bond does not map identical groups onto each other (for example, inverting the wedge $-\text{Cl}$ does not meet a $-\text{Cl}$ on the opposite side).

3. Optical Activity:
   Because the molecule lacks an improper axis of rotation $S_n$ (specifically, it lacks a plane of symmetry $\sigma = S_1$ and an inversion center $i = S_2$), it is chiral. Consequently, the compound is optically active.

Therefore:

• (A) The compound is optically active: Correct
• (B) The compound possesses centre of symmetry: Incorrect
• (C) The compound possesses plane of symmetry: Incorrect
• (D) The compound possesses axis of symmetry: Correct

The correct options are A and D.