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# Quantum Mechanics ## Energy Levels and Quantum Numbers * If n = 2, E2 = 9π2h2 / 8π2am , y = √(3π/8πa) * x → HOMO. * If n = 3, E3 = 16π2h2 / 8π2am , y = √(√(2π/8πa)) * x → HOMO. * If n = 4, E4 = 25π2h2 / 8π2am * If n = 5, E5 = 36 π2h2 / 8π2am , y = √(√(3π/8πa)) * x → LUMO ## HOMO and LUMO * Fo...

# Quantum Mechanics ## Energy Levels and Quantum Numbers * If n = 2, E2 = 9π2h2 / 8π2am , y = √(3π/8πa) * x → HOMO. * If n = 3, E3 = 16π2h2 / 8π2am , y = √(√(2π/8πa)) * x → HOMO. * If n = 4, E4 = 25π2h2 / 8π2am * If n = 5, E5 = 36 π2h2 / 8π2am , y = √(√(3π/8πa)) * x → LUMO ## HOMO and LUMO * For n + 1 e, HOMO - n = n + 1 = 3 * For LUMO, n = n + 1 + 1 = 4 * 42 and geographical presentations ## Nuclear Charge * → nuclear charge * nje * ze = je * = e- ## Mathematical Formula * $d^2ψ / dz^2 + 8π^2m (E - V)ψ / h^2 = 0$