Cis-trans (E/Z) isomerism is a type of geometrical isomerism seen in alkenes. It occurs only when:
1. There is a C=C double bond, and
2. Each of the double bonded carbon atoms is attached to two different groups (i.e., different priority substituents).
Let’s evaluate the options one by one based on this rule:
(a) 1-butene:
Structure: CH\textsubscript{2}=CH–CH\textsubscript{2}–CH\textsubscript{3}
Here, one of the double-bonded carbon atoms (CH\textsubscript{2}) is attached to two identical hydrogen atoms.
Hence, cis-trans isomerism is not possible in 1-butene.
(b) 2-butene-1-ol:
Structure: HO–CH\textsubscript{2}–CH=CH–CH\textsubscript{3}
The double bond is between C2 and C3. C2 is attached to H and CH\textsubscript{2}OH; C3 is attached to H and CH\textsubscript{3}.
Since both double bonded carbons have two different groups, cis-trans (E/Z) isomerism is possible.
(c) 2-chloro-3-hexene:
Structure: CH\textsubscript{3}–CH(Cl)–CH=CH–CH\textsubscript{2}–CH\textsubscript{3}
C3 (CH=) is bonded to C2 (which bears a Cl) and to C4; C4 is attached to two different groups (CH\textsubscript{2}CH\textsubscript{3} and H), and similarly for C3.
Hence, E/Z isomerism is possible.
(d) 4-chloro-2-pentene:
Structure: CH\textsubscript{3}–CH=CH–CH(Cl)–CH\textsubscript{3}
The double bond is between C2 and C3. Check the groups attached:
– C2 is attached to CH\textsubscript{3} and H (fine), but
– C3 is attached to CH(Cl) and H. Here, CH(Cl) and CH\textsubscript{3} may seem different, but the priority order fails due to symmetry on further expansion, making it ambiguous.
However, due to the similar environment and branching, geometrical isomerism is restricted or not well-defined.
Hence, E/Z isomerism is not reliably possible here.