The number of optical isomers in following compound is : __________.

Solution

Chemistry ma’am · 3 steps

Hunt for every chiral carbon, including the ring-fusion ones, then use 2ⁿ since nothing is symmetric.

1. Spot the stereocentres. This is a saturated three-ring system (perhydroanthracene). A ring carbon is chiral when its two paths around the ring are different and its other two groups are also different. Every CH₂ in the rings has two H atoms, so none of them count.

   Carbon	Four different groups	Chiral?
   Carbon carrying CH₃	H, CH₃, ring CH₂, ring-fusion CH	Yes
   Left ring fusion, top	H, three different ring paths	Yes
   Left ring fusion, bottom	H, three different ring paths	Yes
   Right ring fusion carrying Br	Br, three different ring paths	Yes
   Right ring fusion, bottom	H, three different ring paths	Yes

2. Check for symmetry. The CH₃ sits on one end ring and the Br on a fusion carbon of the other. This makes the molecule unsymmetrical, so no meso forms are possible and every combination of configurations is a separate optical isomer.

   Optical isomers = 2ⁿ = 2⁵ = 32

3. So. With 5 stereocentres and no symmetry, the compound has 32 optical isomers.

The common slip: 16. Skipping the Br-bearing ring-fusion carbon because it has no H leaves 4 stereocentres and gives 2⁴ = 16, not 32.

The idea to keep. In fused rings, check every ring-fusion carbon. It is usually chiral even without an H. Use 2ⁿ only after you have confirmed the molecule has no symmetry that could give meso forms.

Answer from the NTA final answer key. Solution by PrepWiser.