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### Electronic System * 2ne system: * HOMO → En = $\frac{n^2h^2}{8ma^2}$ * LUMO n+1 → En+1 = $\frac{(n+1)^2}{8ma^2}$ * ΔΕ. = En-En=$\frac{(n+1)^2h^2}{8ma^2} - \frac{n^2h^2}{8ma^2}$ = $\frac{(n+1)^2h^2}{8ma^2}-(n^2+1+2x-h_2)$ ### Finding ΔELUMO and ΔEHOMO * ΔELUMO - HOMO = $\frac{(2n+1)h^2}...

### Electronic System * 2ne system: * HOMO → En = $\frac{n^2h^2}{8ma^2}$ * LUMO n+1 → En+1 = $\frac{(n+1)^2}{8ma^2}$ * ΔΕ. = En-En=$\frac{(n+1)^2h^2}{8ma^2} - \frac{n^2h^2}{8ma^2}$ = $\frac{(n+1)^2h^2}{8ma^2}-(n^2+1+2x-h_2)$ ### Finding ΔELUMO and ΔEHOMO * ΔELUMO - HOMO = $\frac{(2n+1)h^2}{8ma^2}$ * X H₂C=CH-CH=CH₂, a = 578 pm * △E LOMO - HOMO = 9.02 x 10⁻¹⁹J ### Calculating the frequency and wavenumber * ΔΕ/hc = 4.54 x 10⁴ a ≈ 4.61 x 10⁴ ### Molecular Vibrations * CH₂=CH-CH-CH₂ * Ψ₁(2) → 2x $\frac{4^2}{8mL^2}$ * Ψ₂(2) → 2x $\frac{4₂^2}{8mL^2}$ Date- 09/09/24