Which stereoisomers are optically inactive?

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Step 1: Understand the concept of optical activity. A molecule is optically active if it can rotate plane-polarized light, which typically requires the molecule to be chiral (having non-superimposable mirror images). Optically inactive molecules are either achiral or meso compounds.

Step 2: Analyze the stereoisomers provided in the image. Each structure has four stereocenters (carbon atoms bonded to four different groups). Determine whether each structure is chiral or achiral.

Step 3: Look for symmetry in the molecules. If a molecule has an internal plane of symmetry, it is a meso compound and optically inactive. For example, in structure (b), there is a plane of symmetry dividing the molecule into two identical halves.

Step 4: Compare the configurations of the stereocenters in each molecule. If the stereocenters are arranged in such a way that the molecule is superimposable on its mirror image, it is achiral and optically inactive.

Step 5: Conclude which stereoisomers are optically inactive based on the analysis. Structures with internal symmetry (meso compounds) or those that are achiral will be optically inactive.

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Stereoisomerism

Stereoisomerism refers to the phenomenon where compounds have the same molecular formula and connectivity of atoms but differ in the spatial arrangement of their atoms. This can lead to different physical and chemical properties, including optical activity. The two main types of stereoisomers are enantiomers, which are non-superimposable mirror images, and diastereomers, which are not mirror images.

Optical Activity

Optical activity is the ability of a chiral compound to rotate the plane of polarized light. A compound is considered chiral if it has no plane of symmetry and cannot be superimposed on its mirror image. Only chiral molecules exhibit optical activity, while achiral molecules, which have a plane of symmetry, do not rotate polarized light and are optically inactive.

Chirality and Symmetry

Chirality is a property of a molecule that arises when it has a non-superimposable mirror image, typically due to the presence of a chiral center, often a carbon atom bonded to four different substituents. Molecules that possess a plane of symmetry are achiral and do not exhibit optical activity. Understanding the symmetry of the stereoisomers presented in the question is crucial for determining which are optically inactive.

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