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Part A The color of dyes results from the preferential absorption of certain wavelengths of light. Certain dye molecules consist of symmetric pairs of rings joined at the center by a chain of carbon atoms, as shown in (Figure 1). Electrons of the bonds along the chain of carbon atoms are shared among the atoms in the chain, but are repelled by the nitrogen-containing rings at the end of the chain. These electrons are thus free to move along the chain but not beyond its ends. They look very much like a particle in a one-dimensional box. For the molecule shown, the effective length of the "box" is 0.85 nm. Assuming that the electrons start in the lowest energy state, what is the longest wavelength this molecule will absorb? Express your answer with the appropriate units. На ? A₁ = Value Units Submit Request Answer ▾ Part B Assuming that the electrons start in the lowest energy state, what is the second longest wavelength this molecule will absorb? Express your answer with the appropriate units. ΜΑ x2 = Value Units Submit Request Answer Part C ? Assuming that the electrons start in the lowest energy state, what is the third longest wavelength this molecule will absorb? Express your answer with the appropriate units. με X3 Value Units Submit Request Answer ?

Part A The color of dyes results from the preferential absorption of certain wavelengths of light. Certain dye molecules consist of symmetric pairs of rings joined at the center by a chain of carbon atoms, as shown in (Figure 1). Electrons of the bonds along the chain of carbon atoms are shared among the atoms in the chain, but are repelled by the nitrogen-containing rings at the end of the chain. These electrons are thus free to move along the chain but not beyond its ends. They look very much like a particle in a one-dimensional box. For the molecule shown, the effective length of the "box" is 0.85 nm. Assuming that the electrons start in the lowest energy state, what is the longest wavelength this molecule will absorb? Express your answer with the appropriate units. На ? A₁ = Value Units Submit Request Answer ▾ Part B Assuming that the electrons start in the lowest energy state, what is the second longest wavelength this molecule will absorb? Express your answer with the appropriate units. ΜΑ x2 = Value Units Submit Request Answer Part C ? Assuming that the electrons start in the lowest energy state, what is the third longest wavelength this molecule will absorb? Express your answer with the appropriate units. με X3 Value Units Submit Request Answer ?

Modern Physics
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter5: Matter Waves
Section: Chapter Questions
Problem 13P
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Part A The color of dyes results from the preferential absorption of certain wavelengths of light. Certain dye molecules consist of symmetric pairs of rings joined at the center by a chain of carbon atoms, as shown in (Figure 1). Electrons of the bonds along the chain of carbon atoms are shared among the atoms in the chain, but are repelled by the nitrogen-containing rings at the end of the chain. These electrons are thus free to move along the chain but not beyond its ends. They look very much like a particle in a one-dimensional box. For the molecule shown, the effective length of the "box" is 0.85 nm. Assuming that the electrons start in the lowest energy state, what is the longest wavelength this molecule will absorb? Express your answer with the appropriate units. На ? A₁ = Value Units Submit Request Answer ▾ Part B Assuming that the electrons start in the lowest energy state, what is the second longest wavelength this molecule will absorb? Express your answer with the appropriate units. ΜΑ x2 = Value Units Submit Request Answer Part C ? Assuming that the electrons start in the lowest energy state, what is the third longest wavelength this molecule will absorb? Express your answer with the appropriate units. με X3 Value Units Submit Request Answer ?
Transcribed Image Text:Part A The color of dyes results from the preferential absorption of certain wavelengths of light. Certain dye molecules consist of symmetric pairs of rings joined at the center by a chain of carbon atoms, as shown in (Figure 1). Electrons of the bonds along the chain of carbon atoms are shared among the atoms in the chain, but are repelled by the nitrogen-containing rings at the end of the chain. These electrons are thus free to move along the chain but not beyond its ends. They look very much like a particle in a one-dimensional box. For the molecule shown, the effective length of the "box" is 0.85 nm. Assuming that the electrons start in the lowest energy state, what is the longest wavelength this molecule will absorb? Express your answer with the appropriate units. На ? A₁ = Value Units Submit Request Answer ▾ Part B Assuming that the electrons start in the lowest energy state, what is the second longest wavelength this molecule will absorb? Express your answer with the appropriate units. ΜΑ x2 = Value Units Submit Request Answer Part C ? Assuming that the electrons start in the lowest energy state, what is the third longest wavelength this molecule will absorb? Express your answer with the appropriate units. με X3 Value Units Submit Request Answer ?
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