The incorrect statement regarding the geometrical isomers of 2-butene is :

We need to identify the incorrect statement about geometrical isomers of 2-butene.

2-Butene (CH$$_3$$CH=CHCH$$_3$$) exists as two geometrical isomers due to restricted rotation around the C=C bond:

(i) cis-2-butene: Both methyl groups are on the same side of the double bond.

(ii) trans-2-butene: The methyl groups are on opposite sides of the double bond.

Evaluate each statement:

(1) "cis- and trans-2-butene are not interconvertible at room temperature": This is CORRECT. The energy barrier for rotation around a C=C bond is very high (~250 kJ/mol), preventing interconversion at room temperature.

(2) "cis- and trans-2-butene are stereoisomers": This is CORRECT. They have the same molecular formula and connectivity but differ in the spatial arrangement of atoms. Geometrical isomers are a type of stereoisomers.

(3) "cis-2-butene has less dipole moment than trans-2-butene": This is INCORRECT. In cis-2-butene, the two methyl groups are on the same side, so their bond dipoles add up, resulting in a net dipole moment. In trans-2-butene, the methyl groups are on opposite sides, and their dipoles cancel out, giving a dipole moment of approximately zero. Therefore, cis-2-butene has a HIGHER dipole moment than trans-2-butene.

(4) "trans-2-butene is more stable than cis-2-butene": This is CORRECT. trans-2-butene is more stable because the methyl groups are farther apart, reducing steric strain.

The correct answer is Option (3).