Really uncertain if I\'m doing this question right. Are the first two answers co

Question

Really uncertain if I'm doing this question right. Are the first two answers correct, or am I doing them wrong?

Consider the conjugated molecule decapentaene: How many electrons are in this molecule? There are ten pi electhons un ti molecule If each C-C bond is 135 pm and each C-C bond is 154 pm and assuming the molecule is linear, how long is decapentaene? 35+154 2312 4 ()-1155 pm Let us apply the particle in a box model to the electrons of decapentaene. Because of electron spin two electrons can occupy each wave function. When the molecule is in its ground state (electrons occupy the wave functions that give the lowest possible total energy), what is the quantum number and energy of the wave function that is occupied and has the largest energy? The energy of the particle in a box wave functions are given by: En " 8 ma See other side for rest of assignment

Explanation / Answer

The particle-in-a-box model for qiven molecule is so that electrons are paired in each quantum level. Thus, 10 electrons will fill the first 5 levels and the first transition will be from level 5 6. The ground state quantum number will be ng = 5 and the excited state quantum number will be ne = 6. E = h2 /8ma2 (ne 2 - ng 2 ) = (6.626 x 10-34 Js)2 /8/9.1 x 10-31 kg/(15.1 x 10-10 m)2 (62 - 52 ) = 2.9 x 10-19 J = 14,670 cm-1. The wavelength can be obtained from E = hc/ or = hc/E = (6.626 x 10-34 Js)(2.99 x 108 m)/(2.9 x 10-19 J) = 681 nm. Transition energy = 14,670 cm-1. Transition wavelength = 681 nm.

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