Polyenes and wavelength

[inaccensa]

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Among conjugated polyenes (molecules with alternating
carbon-carbon double and single bonds) why
are those that are longer able to absorb longer wavelengths
of light?
A. Larger molecular orbitals have a lower ground
state.
B. A longer wavelength is better able to interact
with a longer molecular orbital.
C. The larger number of molecular orbitals allows
for smaller energy transitions.
D. Larger molecular orbitals can absorb more
energy.

What basic concept are they testing here? C-C will be longer,but here is another Q. The Sp2 orbitals are all at the same energy level, so the C-C will be at the same energy level as C=C except that its a little longer, is that correct?

 

[loveoforganic]

Is it C? I don't remember this stuff 🙁

 

[eric51]

The answer is C. Basically, they are testing your knowledge of basic Huckel molecular orbital theory. If you have a polyene, you can think of the pi electrons as basically independent of the sigma framework. The more atoms you have, the more p orbitals you start with, and thus the more pi MOs you can make. If you have more pi MOs, this means that the energy between MOs will be lower, and thus they will absorb longer wavelength light (which is lower energy). Look up Huckel method on wikipedia for some more details.
Honestly, this is a pretty hard question, and isn't the type of stuff you would learn in sophomore organic chem. I learned this in physical chemistry, and a little bit again in advanced organic chemistry. This is the kind of question that separates the good MCAT scores from the really awesome MCAT scores.

 

[inaccensa]

you are correct, C is the ans,but now I understand why its the rt choice

 

[raab32]

eric's explanation is spot on, good description man. Also, I took this practice test last week and I remember getting that question right because of something that was stated in the passage.. I'm not completely sure, but I do recognize the question.