Electronic transitions of the molecule butadiene, CH_2 = CH - CH=CH_2, can be ap

Question

Electronic transitions of the molecule butadiene, CH_2 = CH - CH=CH_2, can be approximated using the particle-on-a-line model, if one assumes an electron entire four-carbon chain. a. If a butadiene molecule absorbs a photon with a wavelength 2170 A and electron transitions from the n = 2 to the n = 3 state, what is the approximate length of the C_4H_6 molecule? b. Describe why it is quite remarkable that the predicted length of butadiene based on the particle-on-a-line model is close to the experimental value of 4.8 angstroms. Instead of the boundary conditions defined at x = 0 to a, assume that the limits for x = -a/2 to + a/2. Derive acceptable wave functions for this particle-on-a-line. What are the quantized energies for the particle?

Explanation / Answer

1,3 butadiene

It has 4 p orbitals and has 4 p electrons. Thus, the highest filled orbital is the second level while the lowest unfilled orbital is the third.

Using the particle-in-the-box model, the transition will involve n=2 -> n=3. The energies of these levels are given by the following equation:

E = n2h2/8mL2

So this transition will have the following energy:

=(32 - 22) h2/8mL2

= 6.15 x 10-19 J

l = hc/E

= 3231 Angstroms

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