Does the energy barrier cause the existence of two distinct isomers?
Yes, the energy barrier for rotation about the double bonds in alkenes causes the existence of two distinct isomers.
The π bond of an alkene is stable because the electrons are attracted to both carbon nuclei.
Rotation about the C=C axis breaks the π bond and puts one
This takes energy of about 200 kJ/mol.
The average kinetic energy of a molecule at room temperature is about 4 kJ/mol.
This is not enough energy to break the pi bond, so alkenes like but-2-ene can exist as distinct cis and trans isomers.