Chemistry - STEREO ISOMERISM Question with Solution | TestHub

The central carbon is attached to two $-CH(C{H}_3)Br$ groups ($A$) and two $-CH(C{H}_3)Cl$ groups ($B$), each of which can have an $R$ or $S$ configuration.

Case 1: When both pairs have identical configurations $[(R,R)(R,R)$, $(S,S)(S,S)$, $(R,R)(S,S)$, $(S,S)(R,R)]$, the central carbon is achiral, yielding 4 stereoisomers.

Case 2: When only one pair has different configurations $[(R,R)(R,S)$, $(S,S)(R,S)$, $(R,S)(R,R)$, $(R,S)(S,S)]$, the central carbon remains achiral, yielding 4 stereoisomers.

Case 3: When both pairs have different configurations $[(R,S)$ for $A$ and $(R,S)$ for $B]$, the central carbon is bonded to 4 distinct ligands ($A_R,A_S,B_R,B_S$), creating a chiral center with 2 configurations, yielding 2 stereoisomers.

Total Stereoisomers $=4+4+2=10$.