Concept:
Cis-trans isomerism (geometrical isomerism) is a type of stereoisomerism that arises due to restricted rotation around a double bond. For a compound to exhibit cis-trans isomerism, the following condition must be satisfied:
• Each carbon of the double bond must have two different substituents
Step 1: Understand restriction in double bond
A double bond consists of:
• One sigma bond (free rotation possible)
• One pi bond (restricts rotation)
The presence of $\pi$ bond prevents free rotation, making different spatial arrangements stable.
Step 2: Analyze each option carefully
(A) Pent-1-ene:
\[
CH_2 = CH - CH_2 - CH_2 - CH_3
\]
First carbon has two identical H atoms → does not satisfy condition → no isomerism
(B) But-2-ene:
\[
CH_3 - CH = CH - CH_3
\]
Each carbon has two different groups:
• Left carbon → CH$_3$ and H
• Right carbon → CH$_3$ and H
Thus two distinct arrangements possible:
• Cis: both CH$_3$ on same side
• Trans: CH$_3$ on opposite sides
Hence shows geometrical isomerism.
(C) But-1-ene:
\[
CH_2 = CH - CH_2 - CH_3
\]
First carbon has two H → no isomerism
(D) Propene:
\[
CH_2 = CH - CH_3
\]
Again, first carbon has identical H → no isomerism
(E) Ethene:
\[
CH_2 = CH_2
\]
Both carbons have identical substituents → no isomerism
Step 3: Final deduction
Only But-2-ene satisfies required condition.
Step 4: Visualization insight
Cis-trans isomerism arises because groups cannot rotate around double bond, leading to fixed spatial arrangements.
Final Answer:
\[
\boxed{\text{But-2-ene}}
\]