The organic molecules shown here are derivatives of benzene in which six-membered rings are 'fused' at the edges of the hexagons.
(e) Benzene, naphthalene, and anthracene are colorless, but tetracene is orange. What does this imply about the relative HOMO–LUMO energy gaps in these molecules? See the 'Chemistry Put to Work' box on orbitals and energy.

Verified step by step guidance

1. Step 1: Understand the concept of HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) energy gaps. The color of a molecule is related to the energy gap between these orbitals.
2. Step 2: Recognize that when a molecule absorbs light, an electron is promoted from the HOMO to the LUMO. The energy of the absorbed light corresponds to the energy gap between these orbitals.
3. Step 3: Note that benzene, naphthalene, and anthracene are colorless, indicating that their HOMO-LUMO energy gaps are relatively large, absorbing light in the ultraviolet region which is not visible to the human eye.
4. Step 4: Observe that tetracene is orange, implying that its HOMO-LUMO energy gap is smaller than that of benzene, naphthalene, and anthracene. This smaller gap means it absorbs light in the visible region, specifically in the blue-green part of the spectrum, which makes it appear orange.
5. Step 5: Conclude that as the number of fused benzene rings increases, the HOMO-LUMO energy gap decreases. This trend is due to the increased conjugation and delocalization of π-electrons, which lowers the energy difference between the HOMO and LUMO.

Key Concepts

HOMO-LUMO Gap

The HOMO-LUMO gap refers to the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in a molecule. This gap is crucial in determining a molecule's electronic properties, including its color. A smaller gap typically allows for electronic transitions that can absorb visible light, leading to color, while a larger gap results in colorless compounds.

Aromatic Compounds

Aromatic compounds, such as benzene and its derivatives, are characterized by their stable ring structures and delocalized π-electrons. This delocalization contributes to their unique electronic properties, including stability and specific absorption characteristics. The presence of fused rings, as seen in naphthalene and phenanthrene, can influence the HOMO-LUMO gap and, consequently, the color of the compound.

Color and Electronic Transitions

The color of a compound is often a result of electronic transitions between energy levels when light is absorbed. If a molecule has a small HOMO-LUMO gap, it can absorb visible light, leading to the appearance of color. In contrast, compounds with larger gaps, like benzene and naphthalene, do not absorb visible light and thus appear colorless, while tetracene's orange color suggests a smaller gap allowing for such transitions.