Which of the following alkenes exhibit geometrical isomerism? (a) 2,4 -hexadiene (b) 2 -methyl-1-butene (c) 1 -methylcyclopentene (d) 1,3 -butadiene

Start by drawing the structures of the given alkenes: (a) 2,4-hexadiene, (b) 2-methyl-1-butene, (c) 1-methylcyclopentene, and (d) 1,3-butadiene.

For each alkene, identify if there are two different groups attached to each carbon atom in the double bond. This is a requirement for geometrical isomerism to occur. (a) 2,4-hexadiene: On the first carbon of the first double bond, there are two hydrogen atoms and one ethyl group, while the second carbon has one hydrogen atom, one methyl group, and is a part of the second double bond. The second double bond contains two carbons each with one hydrogen atom and one alkyl group and are part of the first double bond. (b) 2-methyl-1-butene: On the first carbon of the double bond, there are two different groups (one hydrogen atom and one ethyl group), whereas, on the second carbon, there is one hydrogen atom, one methyl group, and the double bond is connected to the carbon carrying another methyl group. (c) 1-methylcyclopentene: On the first carbon of the double bond, there are two different groups (one hydrogen atom and one methyl group), whereas, on the second carbon, there is one hydrogen atom, the double bond is connected to the carbon that's part of the cyclopentene ring. (d) 1,3-butadiene: The first double bond has two carbons, each with one hydrogen atom and one alkyl group. Likewise, the second double bond also has two carbons, each with one hydrogen atom and one alkyl group.

From the analysis in Step 2, we observe that: (a) 2,4-hexadiene does not exhibit geometrical isomerism because the carbons in the double bond are part of another double bond (conjugated diene). (b) 2-methyl-1-butene exhibits geometrical isomerism because each carbon in the double bond has two different groups attached. (c) 1-methylcyclopentene exhibits geometrical isomerism because each carbon in the double bond has two different groups attached. (d) 1,3-butadiene does not exhibit geometrical isomerism as it is a conjugated diene, and has carbons with double bonds that are part of another double bond. Therefore, the alkenes (b) 2-methyl-1-butene and (c) 1-methylcyclopentene exhibit geometrical isomerism.