Final answer:
The longer the conjugated system, the smaller the energy difference between the HOMO and LUMO. This is due to increased delocalization of electrons in larger conjugated systems.
Step-by-step explanation:
The question pertains to the energy difference between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) in the context of conjugated systems in organic chemistry. In a conjugated system, where π-bonds are delocalized through alternating single and double bonds, the longer the conjugated system, the smaller the energy difference becomes between the HOMO and LUMO levels. This is because the addition of more p-orbitals to the conjugated system allows for greater delocalization of the electrons, which in turn lowers the energy of the LUMO and raises the energy of the HOMO, thus narrowing the gap. An example of this can be seen in the absorption of UV light by 1,3-butadiene, which has a longer conjugated system than ethene (a molecule with an isolated pi bond) and consequently a smaller HOMO-LUMO gap, evidenced by its absorption at 217 nm.