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Chapter 9: Problem 108

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?

Short Answer

Expert verified
Lycopene, responsible for the red color in tomatoes, has a larger HOMO-LUMO gap than curcumin, responsible for the yellow color in turmeric. This is because red light is less energetic than yellow light, and a less energetic color corresponds to a larger HOMO-LUMO gap.

Step by step solution

01

Identify the colors and wavelengths of lycopene and curcumin

Lycopene is responsible for the red color in tomato, and curcumin is responsible for the yellow color in turmeric. According to the visible light spectrum, red light has a longer wavelength (approx. 620-750 nm) and lower energy than yellow light (approx. 570-590 nm).
02

Relate the energy of colors to the HOMO-LUMO gap

According to the relationship between color and energy gap mentioned in the analysis, a less energetic color has a larger HOMO-LUMO gap and a more energetic color has a smaller HOMO-LUMO gap. Since red light (lycopene) is less energetic than yellow light (curcumin), the HOMO-LUMO gap is expected to be larger for lycopene than for curcumin.
03

Conclusion

Comparing their colors, lycopene (red) is less energetic than curcumin (yellow). Hence, lycopene has a larger HOMO-LUMO gap than curcumin.

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Most popular questions from this chapter

(a) The \(\mathrm{PH}_{3}\) molecule is polar. Does this offer experimental proof that the molecule cannot be planar? Explain. (b) It turns out that ozone, \(\mathrm{O}_{3}\), has a small dipole moment. How is this possible, given that all the atoms are the same?

Consider the \(\mathrm{H}_{2}^{+}\) ion. (a) Sketch the molecular orbitals of the ion and draw its energy-level diagram. (b) How many electrons are there in the \(\mathrm{H}_{2}^{+}\) ion? (c) Write the electron configuration of the ion in terms of its MOs. (d) What is the bond order in \(\mathrm{H}_{2}^{+}\) ? (e) Suppose that the ion is excited by light so that an electron moves from a lower-energy to a higher- energy MO. Would you expect the excited-state \(\mathrm{H}_{2}^{+}\) ion to be stable or to fall apart? (f) Which of the following statements about part (e) is correct: (i) The light excites an electron from a bonding orbital to an antibonding orbital, (ii) The light excites an electron from an antibonding orbital to a bonding orbital, or (iii) In the excited state there are more bonding electrons than antibonding electrons?

Antibonding molecular orbitals can be used to make bonds to other atoms in a molecule. For example, metal atoms can use appropriate \(d\) orbitals to overlap with the \(\pi_{2}^{*}\), orbitals of the carbon monoxide molecule. This is called \(d-\pi\) backbonding. (a) Draw a coordinate axis system in which the \(y\) -axis is vertical in the plane of the paper and the \(x\) -axis horizontal. Write ${ }^{4} \mathrm{M}^{\prime \prime}$ at the origin to denote a metal atom. (b) Now, on the \(x\) -axis to the right of \(\mathrm{M}\), draw the Lewis structure of a CO molecule, with the carbon nearest the \(\mathrm{M}\). The CO bond axis should be on the \(x\) -axis. (c) Draw the \(\mathrm{CO} \pi_{2 p}^{*}\) orbital, with phases (see the "Closer Look" box on phases) in the plane of the paper. Two lobes should be pointing toward M. (d) Now draw the \(d_{x y}\) orbital of \(\mathrm{M}\), with phases. Can you see how they will overlap with the \(\pi_{2 p}^{*}\) orbital of $\mathrm{CO} ?\( (e) What kind of bond is being made with the orbitals between \)\mathrm{M}$ and \(\mathrm{C}, \sigma\) or \(\pi ?\) (f) Predict what will happen to the strength of the CO bond in a metal-CO complex compared to CO alone.

What is the hybridization of the central atom in (a) \(\mathrm{PBr}_{5}\), (b) \(\mathrm{CH}_{2} \mathrm{O},\) (c) \(\mathrm{O}_{3},(\mathbf{d}) \mathrm{NO}_{2} ?\)

(a) What is the difference between a localized \(\pi\) bond and a delocalized one? (b) How can you determine whether a molecule or ion will exhibit delocalized \(\pi\) bonding? (c) Is the \(\pi\) bond in \(\mathrm{NO}_{2}^{-}\) localized or delocalized?
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