MHT CET · Chemistry · General Organic Chemistry

If \(n\) is the number of asymmetric carbon atoms, the number of optical isomers possible is given by formula

A \(\mathrm{n}^{2}\)
B \(\frac{\mathrm{n}}{2}\)
C \(2 \mathrm{n}\)
D \(2^{n}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2^{n}\)

Step-by-step Solution

Detailed explanation

The general formula for calculating stereoisomer is: \(2^{\text {n }}\), where \(\mathrm{n}\) is the number of chiral centers.
Stereoisomers are compounds with the same chemical formula but different spatial arrangement and chiral centers are carbons that are bonded to \(4\) different groups. So, the possible no of optical isomers can be \(2^{n}\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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