Question

If ‘n’ represents total number of asymmetric carbon atoms in a compound, the possible number of optical isomers of the compound is:
(A) $2n$
(B) ${n^2}$
(C) ${2^n}$
(D) $2n + 2$

Answer 1

Hint: To answer this question we must first understand what optical isomers are. We should also learn to calculate the number of optical isomers of a compound from its chiral carbons.

Complete step by step answer:
Isomers are actually molecules with the same molecular formula but different spatial arrangement. Optical isomerism is a form of stereoisomerism. They rotate a plane polarized light in two different directions. They have a non superimposable mirror image relationship with each other.
We should remember that a carbon atom with four different groups attached to it has no plane of symmetry. This is called an asymmetric or chiral carbon. Only these are able to form optical isomers.
The number of optical isomers in a compound is determined by the number of chiral centers in it. A chiral centre is a carbon atom that is bonded to four different molecules or atoms.
Each chiral centre will result in two different optical isomers.

Hence, the correct answer is Option (A) 2n.

Additional information:
Whenever we are given a compound, we just have to draw it and then count the number of chiral carbons and multiply it by 2 to get the total number of optical isomers.

Note: We should note that dextrorotation and levorotation simply refers to the rotation of an optically active compound by a plane polarized light. From the point of view of the observer, a dextrorotatory compound rotates the light clockwise towards the right side whereas a levorotatory compound rotates in anticlockwise towards the left side.