Final answer:
A smaller energy gap between HOMO and LUMO results in the absorption of longer wavelengths of light. The lower the energy gap, the lower the energy required for an electronic transition, thus longer wavelengths, such as those in the visible spectrum, are absorbed.
Step-by-step explanation:
A smaller energy gap between HOMO and LUMO results in longer wavelengths of light being absorbed by a molecule. In the context of molecular orbital theory, HOMO stands for highest occupied molecular orbital and LUMO stands for lowest unoccupied molecular orbital. When a molecule absorbs a photon of light, if the energy of the photon matches the energy gap (ΔE) between the HOMO and LUMO, an electron can be excited from the HOMO to the LUMO.
This process is responsible for the absorption of specific wavelengths of light. When the energy gap is smaller, the molecule can absorb light of longer wavelengths, which have lower energy, such as those in the visible region rather than the ultraviolet (UV) region. Conversely, larger energy gaps correspond to absorption of shorter, higher-energy wavelengths in the UV region. For instance, molecules in beta-carotene absorb light in the visible spectrum, making carrots appear orange.
In general, when comparing molecules with different extents of conjugation, more extended pi systems have smaller HOMO-LUMO energy gaps. This leads to absorption at longer wavelengths, which is why materials with extensive conjugation can be colored.1