Molecules that are brightly colored have a small energy gap between filled and empty electronic states (the HOMOLUMO gap; see Exercise 9.104). Suppose you have two samples, one is lycopene which is responsible for the red color in tomato, and the other is curcumin which is responsible for the yellow color in turmeric. Which one has the larger HOMO-LUMO gap?

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Step 1: Understand the concept of 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). This gap is directly related to the color of a molecule. The smaller the gap, the longer the wavelength of light absorbed, and the redder the color.

Step 2: Recall that the color of light absorbed by a molecule is complementary to the color we see. For example, if a molecule absorbs blue light, it will appear yellow to our eyes. If it absorbs green light, it will appear red.

Step 3: Apply this knowledge to the given problem. Lycopene, which is red, absorbs green light. Curcumin, which is yellow, absorbs blue light.

Step 4: Remember that the energy of light is inversely proportional to its wavelength. Blue light has a shorter wavelength and therefore higher energy than green light.

Step 5: Conclude that since curcumin absorbs higher energy light (blue) than lycopene (green), it must have a larger HOMO-LUMO gap.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 the absorption of visible light, resulting in vibrant colors, while a larger gap may lead to less intense colors.

Color and Energy Absorption

The color of a molecule is determined by the wavelengths of light it absorbs. When a molecule absorbs light, electrons are excited from the HOMO to the LUMO. The specific energy of the absorbed light corresponds to the HOMO-LUMO gap; thus, molecules with smaller gaps absorb longer wavelengths (redder colors), while those with larger gaps absorb shorter wavelengths (bluer colors).

Molecular Structure and Color

The molecular structure, including the presence of conjugated systems (alternating double and single bonds), significantly influences the HOMO-LUMO gap. Conjugation lowers the energy of the HOMO and raises the energy of the LUMO, resulting in a smaller gap and more vivid colors. Lycopene and curcumin have different structures, which affects their respective HOMO-LUMO gaps and, consequently, their colors.

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