Final answer:
The longer the conjugated system, the smaller the energy difference between the HOMO and LUMO, which allows for the absorption of light with longer wavelengths.
Step-by-step explanation:
The longer the conjugated system, the smaller the energy difference between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital). In chemistry, particularly in the study of molecular orbitals, a conjugated system refers to a system of connected p-orbitals with delocalized electrons. For instance, 1,3-butadiene, which has a conjugated double-bond system, absorbs UV light with a wavelength of 217 nm, indicating a smaller energy gap compared to an isolated pi-bond system.
As the conjugation in a molecule increases, the number of molecular orbitals derived from the pi bonds increases, and they become more closely spaced. This leads to a decrease in the energy difference between the HOMO and LUMO, facilitating the absorption of longer wavelengths (that is, lower energy) of light.