Concept:
Optical isomerism arises when a molecule contains a chiral (asymmetric) carbon atom.
A carbon atom is said to be chiral when it is attached to four different groups. Such molecules exist as non-superimposable mirror images (enantiomers).
Step 1: Write structures of all given alcohols.
• (A) 1-pentanol: \(CH_3-CH_2-CH_2-CH_2-CH_2OH\)
• (B) 2-pentanol: \(CH_3-CH(OH)-CH_2-CH_2-CH_3\)
• (C) 3-pentanol: \(CH_3-CH_2-CH(OH)-CH_2-CH_3\)
• (D) 2-methyl-2-butanol: \(CH_3-C(OH)(CH_3)-CH_2-CH_3\)
• (E) 2,2-dimethyl-1-propanol: highly branched structure
Step 2: Check for chiral carbon in each.
(A) 1-pentanol:
OH is at terminal carbon → that carbon has two H atoms → not chiral → no optical isomerism.
(B) 2-pentanol:
Focus on carbon 2:
\[
CH_3-CH(OH)-CH_2-CH_2-CH_3
\]
Substituents on this carbon:
• \(H\)
• \(OH\)
• \(CH_3\)
• \(C_3H_7\)
All four are different → carbon is chiral → optically active.
(C) 3-pentanol:
Structure is symmetric:
\[
CH_3-CH_2-CH(OH)-CH_2-CH_3
\]
Left and right sides identical → not chiral.
(D) 2-methyl-2-butanol:
Central carbon has two identical \(CH_3\) groups → not chiral.
(E) 2,2-dimethyl-1-propanol:
Highly symmetric → no chiral carbon.
Final Conclusion:
\[
\boxed{\text{Only 2-pentanol shows optical isomerism}}
\]