Concept: Geometrical isomerism (also known as cis-trans isomerism) is a type of stereoisomerism that can occur in molecules with restricted rotation around a bond, typically a carbon-carbon double bond (\(C=C\)) or in cyclic compounds.
For geometrical isomerism around a \(C=C\) double bond, two conditions must be met:
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(W) There must be restricted rotation around the \(C=C\) bond (which is inherent to double bonds).
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(X) Each carbon atom of the double bond must be attached to two different atoms or groups.
Step 1: Analyze the structures of the given compounds
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(Y) (1) Butanol-2 (2-Butanol): \(CH_3-CH(OH)-CH_2-CH_3\). This is an alcohol and does not have a \(C=C\) double bond relevant for geometrical isomerism in its main chain. (It has a chiral center and can exhibit optical isomerism, but not geometrical isomerism in the typical alkene sense).
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(Z) (2) Butene-1 (1-Butene): \(CH_2=CH-CH_2-CH_3\).
Let's look at the carbons of the double bond (\(C_1=C_2\)):
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([) \(C_1\) is attached to two Hydrogen atoms (H, H). Since these two groups are identical, geometrical isomerism is not possible around this bond.
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(\) \(C_2\) is attached to a Hydrogen atom (H) and an Ethyl group (\(-CH_2CH_3\)).
Since \(C_1\) has two identical groups (H, H), 1-Butene does not exhibit geometrical isomerism.
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(]) (3) Butene-2 (2-Butene): \(CH_3-CH=CH-CH_3\).
Let's look at the carbons of the double bond (\(C_2=C_3\)):
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(^) \(C_2\) is attached to a Hydrogen atom (H) and a Methyl group (\(-CH_3\)). These are different.
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(_) \(C_3\) is attached to a Hydrogen atom (H) and a Methyl group (\(-CH_3\)). These are different.
Since both \(C_2\) and \(C_3\) are each attached to two different groups, 2-Butene can exhibit geometrical isomerism (cis-2-butene and trans-2-butene).
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(`) {cis}-2-Butene: Methyl groups are on the same side of the double bond.
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(a) {trans}-2-Butene: Methyl groups are on opposite sides of the double bond.
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(b) (4) Butyne-1 (1-Butyne): \(HC \equiv C-CH_2-CH_3\). This molecule has a carbon-carbon triple bond (\(C \equiv C\)). Triple bonds are linear around the alkyne carbons and do not exhibit geometrical isomerism of the cis-trans type.
Step 2: Identifying the compound exhibiting geometrical isomerism
Based on the analysis, Butene-2 (2-Butene) meets the criteria for geometrical isomerism.