The number of optical isomers in following compound is: ________

1. Identifying the Chiral Centers (Stereocenters):

   A carbon atom is considered a chiral center if it is bonded to four completely different groups. In the given structure, the positions marked with a star ($$\star$$) denote the chiral carbons:

   • Two chiral centers are located at the ring junctions between the first (left) and second (middle) rings.
   • Two chiral centers are located at the ring junctions between the second (middle) and third (right) rings.
   • One chiral center is located at the top position of the third (rightmost) ring.

   Counting all the starred positions gives the total number of chiral centers, $$n = 5$$.




2. Checking for Molecular Symmetry:

   Because of the additional substitution/stereocenter on the rightmost ring, the molecule lacks any plane of symmetry ($$\sigma$$) or center of inversion ($$i$$). The molecule is completely unsymmetrical.




3. Calculating the Number of Optical Isomers:

   For a completely unsymmetrical molecule with $$n$$ chiral centers, all possible stereoisomers are optically active (forming pairs of enantiomers), and the formula to calculate the total number of optical isomers is:

   $$\text{Number of Optical Isomers} = 2^n$$

   Substituting $$n = 5$$ into the formula:

   $$\text{Number of Optical Isomers} = 2^5 = 32$$

Conclusion:

The unsymmetrical nature of the compound with 5 distinct chiral centers results in a total of 32 stereoisomers, all of which are optically active.

Answer: 32