Step 1: Understanding the Concept:
Geometrical isomerism (cis-trans isomerism) occurs in alkenes when rotation around the carbon-carbon double bond (\(C=C\)) is restricted.
For a molecule to exhibit geometrical isomerism, each of the two doubly bonded carbon atoms must be attached to two different groups.
Step 2: Key Formula or Approach:
Examine the substituents on each carbon of the double bond.
If the arrangement is \(R_1R_2C=CR_3R_4\), then geometrical isomerism is possible only if \(R_1 \neq R_2\) and \(R_3 \neq R_4\).
Step 3: Detailed Explanation:
1. But-1-ene (\(CH_2=CH-CH_2-CH_3\)): The first carbon is attached to two hydrogen atoms (identical). Thus, it cannot show geometrical isomerism.
2. But-2-ene (\(CH_3-CH=CH-CH_3\)): The first double-bonded carbon is attached to \(H\) and \(CH_3\). The second double-bonded carbon is also attached to \(H\) and \(CH_3\). Since both carbons have two different groups, it exists as cis and trans isomers.
3. Propene (\(CH_2=CH-CH_3\)): The first carbon is attached to two hydrogen atoms. No geometrical isomerism possible.
4. Ethene (\(CH_2=CH_2\)): Both carbons are attached to identical hydrogen atoms. No geometrical isomerism possible.
Step 4: Final Answer:
The compound that shows geometrical isomerism is But-2-ene.