Lecture 4 - Lecture 4 Quantum Theory I: One-electron Atoms...

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Unformatted text preview: Lecture 4 Quantum Theory I: One-electron Atoms p. 202 Franhaufer Lines ~ 700 sharp absorption lines ∞ 3 5 4 H-Atom, One-Electron Ions ­R 9 Spectroscopy Spectroscopy 2 Balmer Balmer UV Lyman ∞ 3 2 λ ~ 657nm 657nm 4 2 λ ~ 487nm ~ 5 2 λ ~ 435nm 435nm ­R 4 ∞ 1 © 2001 A.Pines,M.Kubinec,UC Regents ­R ∞ L6­5 Energy of Transitions ­1 En= n2 R ∞ R = 2.18 x 10 J N∞R = 1312 kJmol ∞ ΔE= ­ R ∞ 1 nf 2 1 ni 2 ni ΔE = hν nf Cowboy Chemistry The Study of Vigorous Chemical Reactions Energy Chemical Reactions Ea Reactants Kinetics Ea = Activation Energy 2H2 + ΔH 2 2H2O Thermodynamics O Exo Exo Products Reaction Coordinate Physics: pre-1900 Particles and Waves ­localized ­momentum -delocalized e­ p=mv λ Wave h=6.62 x 10­34 Js v Particle h p= λ Duality h λ= p De Broglie Wavelengths Particle Photon (yellow) Photon ( e­ (v ~ 10 m sec ) Na (80K, v~300 m sec ) v~300 m sec Baseball (170g, v~40 m sec ) de Broglie λ (nm) (nm) ~ 600 ~ 6 ~ 0.06 ~ 6x10­26 Lecture 4 Quantum Theory I: One-electron Atoms p. 202 BLACKBOARD Fig. 5-1, p. 171 x Coordinates and quantum numbers z Ψ(r,,θ , φ)) (r , φ e ­ Three spherical polar coordinates θ r y | Ψ| : Probability ( e ) : Probability ( e φ n, ℓ, mℓ Three quantum numbers Wave Functions Wave Table 5-2, p. 175 Quantum Numbers Q.N. n : Principal values orbital property n: 1, 2, 3 . . . ℓ: 0 (s), 1 (p), 2 (d), n­1 Energy Shape Total nodes =n­1 ℓ : Angular Momentum mℓ : Magnetic Angular nodes = ℓ Orientation mℓ: ­ℓ, ­(ℓ­1),..,0,..,(ℓ­1), ℓ Orbital Energies n : Principal Q. N. 2 n ∞ 3 2 n: 1, 2, 3 . . . Ionized E 0 ­R ­R∞ 4 ∞ ­Z R∞ En = n2 R∞ = 2.18 x 10­18 J = 3.29 x1015 Hz N0R∞ = 1312 kJmol­1 9 1 Ground ­R ∞ The Quantum Stairway Fig. 5-2, p. 173 One-Electron Atoms One-Electron Atoms n = 1 ℓ = 0 (s) m ℓ = 0 z 1s + x y x Radial Node n = 2 ℓ = 0 (s) m ℓ = 0 z + 2s ­ y mℓ = ­1, +1 z x Angular Node n=2 ℓ = 1 (p) z y mℓ = 0 z z + 2p ­ y ­ 2p + y x x x n = 3 ℓ = 0, 1, 2 3s, 3p, 3d Orbitals ℓ = angular nodes; n­1 = total nodes + 2p ­ y Fig. 5-9, p. 181 This lecture is Terminated!!! ...
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