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A chiral carbon atom (also known as asymmetric carbon atom) is a carbon atom with four different groups (or atoms) attached to it in an organic molecule.
If a molecule has a chiral atom, it and the molecule of its mirror image are two isomers called enantiomers. Each enantiomer can rotate the plane of polarization of plane polarized light, and this is said to be optically active. Rotations of plane-polarized light by the pure samples of enantiomers are equal in magnitude but opposite in sign (but all other physical properties of the two enantiomers are identical).
A racemic mixture (or racemate) is a 50:50 mixture of a pair of enantiomers. A racemic mixture shows no rotation of the plane-polarized light, because their optical activities cancel each other.