Thank you in advance! 1. The formulas for the 1-dimensional particle in a box ha

Question

Thank you in advance!

1. The formulas for the 1-dimensional particle in a box have been used to approximate the energies of the electrons in linear conjugated molecules. For example, butadiene: CH2-CH-CH=CH2 is approximated as a linear "box" with a length equal to the sum of the bond lengths-0.424 nm in this case. The resulting energy levels are "filled" with the available electrons in this case) with two per level (spin-up and spin-down). Estimate the absorption frequency of butadiene with this model. The experimentally observed value is 5.72 eV.

Explanation / Answer

1D energy = n2h 2 /8mL2For buta diene

E = E3 E2 = (32 2 2 ) h 2 /8mL2 = 5 ( (6.626 x 10-34)2/(8x 9.1 x10 -31 x (4.24 x 10-10)2 ) = 0.1677x 10-17 = 16.77 x 10-19 = 10.48 eV

experimental value is much lower than that of the calculated one due to delocalization.

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