Lecture 5 - Lecture 5 Quantum Theory II: MANY-electron...

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Unformatted text preview: Lecture 5 Quantum Theory II: MANY-electron Atoms p. 202 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 Lecture #4: Quantum Theory of Atoms Fig. 4-17, p. 135 Overhead 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 ∞ Energy Levels Energy n ∞ 3 2 Ionized E 0 ­R ­R∞ 4 ∞ ℓ=0 mℓ=­1 ℓ=1 0 1 ­2 ­1 0 1 ℓ=2 2 9 3s 2s 3d (5 orbitals) 3p 3p 3p 2p 2p 2p 1 Ground ­R 1s Notation: nℓmℓ L8­8 ∞ © A.Pines,M.Kubinec UCB 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 Ψ(r,θ ,φ) = Rn,l(r)Y , (θ ,φ) lm radial angular P = | Ψ| r drdθ dφ Prob density Volume element Table 5-2, p. 175 Overhead Spectra of Multi-Electron Spectra Atoms????? Atoms????? ℓ=0 ℓ=1 ℓ=2 Shielding ­ + 2p 2s 4s 3s 2s 1s 4p 3p 3p 2p 3d E(3d) > E(4s) E(2p) > E(2s) 1s Lecture 5 Quantum Theory II: MANY-electron Atoms p. 202 Electron Spin, Magnetism Electron Spin Little Magnet N S Quantized Spin Q.M. Classical Q.M. ms=­1/2 ms=1/2 “Spin Down” “Spin Up” Electron 4 Q.N.s n, ℓ , mℓ , ms Spectra of Multi-Electron Spectra Atoms Atoms ℓ=0 ℓ=1 ℓ=2 Shielding ­ + 2p 2s 4s 3s 2s 1s 4p 3p 3p 2p 3d E(3d) > E(4s) E(2p) > E(2s) 1s BLACKBOARD Orbital Energies, Shielding ∞ 3 2 H (kJ/mol) 328 1312 2372 5248 IE + 21 1 ∞ Many­e­ system One­e­ system ∞ ∞ ∞ He (1s ) 2p6 ) He (1s 36 He 4 4 2 3 3 2 2 1 1 1 E= Z2eff n2 R ∞ 11 This lecture is Terminated!!! Have a WILD WEEKEND!!!!! ...
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