Question

How many stereoisomers are possible for the following molecule?

A.$4$
B.$8$
C.$12$
D.$16$

Answer 1

We know that stereoisomerism is a kind of isomerism where structure differs in spatial arrangement of atoms rather than atom to atom connectivity. By finding the chiral centers followed by making different arrangement substituents around those chiral centers and then classify them as enantiomers and meso compounds.
Formula Used:
To calculate the number of stereoisomers the following formula can be used: Number of stereoisomers $={{2}^{n}}-$ meso structures.

Complete answer:
As we know that the isomers which have the same molecular formula but have a difference in the spatial arrangement then they are called stereoisomers and the isomerism is called stereoisomerism. Two kinds of stereoisomers are present enantiomers and diastereomers. Stereoisomers are those compounds which have the same molecular formula but different arrangement of atoms in three-dimensional space.
In stereochemistry, stereoisomerism or spatial isomerism is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms but differ in the three-dimensional orientations of their atoms in space. In the given compound we can see that three stereo genic centers are available.
Thus, the number of stereoisomers $={{2}^{n}}-$ meso structures, where n is the number of chiral centers. The number of stereoisomers is ${{2}^{3}}$ which is in total eight stereoisomers.

Therefore, the correct answer is option A.

Note:
Remember that the stereo genic center atoms present in this compound where the stereo center atom is that compound which has all the three different groups attached with itself like a chiral carbon atom