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### Find HOMO and LOMO Egap for H-atom energy levels system? $$E = \frac{(n + \frac{1}{2})^2 h^2}{8\pi^2 a m}$$ $$ψ = \sqrt{\frac{2}{a}} sin(\frac{(n + \frac{1}{2})\pi x}{a})$$ $$h = \frac{4\pi^2 h^2 a}{8\pi^2 a m}$$ Where: * n = 1, E₁ = 4π²h²a / 8π²am = 2h² / 8π²am = h² / 4π²am * n = 2, E₂ =...

### Find HOMO and LOMO Egap for H-atom energy levels system? $$E = \frac{(n + \frac{1}{2})^2 h^2}{8\pi^2 a m}$$ $$ψ = \sqrt{\frac{2}{a}} sin(\frac{(n + \frac{1}{2})\pi x}{a})$$ $$h = \frac{4\pi^2 h^2 a}{8\pi^2 a m}$$ Where: * n = 1, E₁ = 4π²h²a / 8π²am = 2h² / 8π²am = h² / 4π²am * n = 2, E₂ = 5π²h²a / 8π²am = 5h² / 8π²am * n = 3, E₂ = 9π²h²a / 8π²am = 9h² / 8π²am * n = 4, E₂ = 13π²h²a / 8π²am = 13h² / 8π²am * n = 5, E₂ = 25π²h²a / 8π²am = 25h² / 8π²am #### HOMO and LOMO HOMO (Highest Occupied Molecular Orbital) * n = 2 → HOMO LOMO (Lowest Unoccupied Molecular Orbital) * n = 2 + 1 → LOMO